hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Highly cototient number
In number theory, a branch of mathematics, a highly cototient number is a positive integer  which is above 1 and has more solutions to the equation

than any other integer below  and above 1. Here,  is Euler's totient function. There are infinitely many solutions to the equation for

= 1

so this value is excluded in the definition. The first few highly cototient numbers are:

2, 4, 8, 23, 35, 47, 59, 63, 83, 89, 113, 119, 167, 209, 269, 299, 329, 389, 419, 509, 629, 659, 779, 839, 1049, 1169, 1259, 1469, 1649, 1679, 1889, ... (sequence A100827 in the OEIS)

Many of the highly cototient numbers are odd.

The concept is somewhat analogous to that of highly composite numbers. Just as there are infinitely many highly composite numbers, there are also infinitely many highly cototient numbers. Computations become harder, since integer factorization becomes harder as the numbers get larger.

On-Line Encyclopedia of Integer Sequences
The On-Line Encyclopedia of Integer Sequences (OEIS) is an online database of integer sequences. It was created and maintained by Neil Sloane while researching at AT&T Labs. He transferred the intellectual property and hosting of the OEIS to the OEIS Foundation in 2009, and is its chairman.

OEIS records information on integer sequences of interest to both professional and amateur mathematicians, and is widely cited. As of November 2025, it contains over 390,000 sequences, and is growing by approximately 30 entries per day.

Each entry contains the leading terms of the sequence, keywords, mathematical motivations, literature links, and more, including the option to generate a graph or play a musical representation of the sequence. The database is searchable by keyword, by subsequence, or by any of 16 fields. There is also an advanced search function called SuperSeeker which runs a large number of different algorithms to identify sequences related to the input.
Manuel de Mier y Terán
José Manuel Rafael Simeón de Mier y Terán (February 18, 1789 — July 3, 1832), generally known as  Manuel de Mier y Terán, was a noted military and political figure during the Mexican War of Independence and during the era of the First Republic serving in the Mexican congress and as Minister of War. He made an inspection of Texas on behalf of the government and was placed in charge of securing the area after the Mexican government banned further American immigration in 1830.

He was at one point considered a potential candidate for the Mexican presidency. However, health problems and despair over the nation's political situation drove him to commit suicide in 1832 during a revolution against the government of Anastasio Bustamante.

Plan of Veracruz (1832)
In the history of Mexico, the Plan of Veracruz was a proclamation released on January 2, 1832, by the military garrison of Veracruz. The initial goal was simply to remove unpopular ministers from the cabinet of  President Anastasio Bustamante, but later expanded into a year-long civil war within the First Mexican Republic that ended with the ousting of Bustamente and the recognition of Manuel Gómez Pedraza as president.
Begoña Blasco
Begoña Blasco (born 30 April 1960) is a former Spanish rhythmic gymnast. She won the bronze medal with ribbon at the World Championships in Madrid in 1975. That same year she became the first national champion of Spain.

Spanish Rhythmic Gymnastics Championships
The Spanish Rhythmic Gymnastics Championship is the most important national rhythmic gymnastics competition in Spain. It is organized annually since 1975 by the Royal Spanish Federation of Gymnastics and today, since 2010, it is called the Spanish Championship of Individuals, Clubs and Autonomies. It is currently held in June and alongside the Spanish Men's Individual Championship.
Polly Peck
Polly Peck International (PPI) was a small British textile company which expanded rapidly in the 1980s and became a constituent of the FTSE 100 Index before collapsing in 1991 with debts of £1.3 billion, eventually leading to the flight of its CEO, Asil Nadir, to Northern Cyprus in 1993. Polly Peck was one of several corporate scandals that led to the reform of UK company law, resulting in the early versions of the UK Corporate Governance Code.

On 26 August 2010, Nadir returned to the UK to try to clear his name. Prosecutors alleged that he stole more than £150 million from Polly Peck and he faced trial on 13 specimen charges totalling £34 million. Nadir was found guilty on 10 counts of theft totalling £29 million. On 23 August 2012 at the Old Bailey, he was sentenced to 10 years in prison.

FTSE 100 Index
The Financial Times Stock Exchange 100 Index, also called the FTSE 100 Index, FTSE 100, FTSE or, informally, the "Footsie" /ˈfʊtsi/, is one of the United Kingdom's best-known stock market indices and represents the 100 most highly capitalised blue chips listed on the London Stock Exchange.
Brihad Bhagavatamrita
Brihad-bhagavatamrita is a sacred text for followers of the Hindu tradition of Gaudiya Vaishnavism. Along with Hari-bhakti-vilasa, it is one of the most important works of Vaishnava theologian Sanatana Goswami.  While Hari-bhakti-vilasa sets out guidance for Vaishnava behavior and ritual, Brihad-bhagavatamrita contains an analysis of the teachings of Chaitanya from an ontological and metaphysical perspective.

Sanatana Goswami
Sanatana Goswami (Sanskrit: सनातन गोस्वामी, IAST: Sanātana Gosvāmī; Bengali: সনাতন গোস্বামী; 1488–1558) was a principal follower of Chaitanya Mahaprabhu. Sanatana wrote a number of  works in the bhakti tradition of Gaudiya Vaishnavism and was the senior most of the influential Six Goswamis of Vrindavan, among whom was his brother Rupa Goswami.
Mendip Way
The Mendip Way is an 80-kilometre (50 mi) long-distance footpath across the Mendip Hills from Weston-super-Mare to Frome. It is divided into two sections.

The West Mendip Way was opened in 1979 and starts at the Bristol Channel at Uphill Cliff. It climbs the Mendip escarpment affording views over the Somerset Levels. It then crosses the central Mendip plateau leading down to Cheddar Gorge and on to Wells. Most of the western section is within the Mendip Hills Area of Outstanding Natural Beauty. From there the East Mendip Way continues through Shepton Mallet to Frome.

The Mendip Way connects with the Macmillan Way, Monarch's Way, and Samaritans Way South West. The western trailhead of the Limestone Link is within 2 kilometres (1.2 mi) of the Mendip Way near Shipham.

Cheddar Gorge
Cheddar Gorge is a limestone gorge in the Mendip Hills, near the village of Cheddar, Somerset, England. The gorge is the site of the Cheddar show caves, where Great Britain's oldest complete human skeleton, Cheddar Man, estimated to be 9,000 years old, was found in 1903. Older remains from the Upper Late Palaeolithic era (12,000–13,000 years ago) have been found. The caves, produced by the activity of an underground river, contain stalactites and stalagmites. The gorge is part of a Site of Special Scientific Interest called Cheddar Complex.

Cheddar Gorge, including the caves and other attractions, has become a tourist destination. In a 2005 poll of Radio Times readers, following its appearance on the television programme Seven Natural Wonders (2005), Cheddar Gorge was named as the second greatest natural wonder in Great Britain, surpassed only by Dan yr Ogof caves.
The gorge attracts about 500,000 visitors per year.
Darwin and the Science of Evolution
Darwin and the Science of Evolution (UK title: Charles Darwin: The Scholar Who Changed Human History; French: Darwin et la science de l'évolution) is a 2000 illustrated biography of Charles Darwin, and a monograph on his theory of evolution. Written by the French historian of science Patrick Tort, and published in pocket format by Éditions Gallimard as the 397th volume in their "Découvertes" collection (known as "Abrams Discoveries" in the United States, and "New Horizons" in the United Kingdom). The book was adapted into a documentary film of the same title in 2002.

Livre d'art
Livres d'art (French for art books or books of art), otherwise referred to as livres de galerie (French for gallery books), are books in which the illustration holds a predominant place in relation to the text. They often require high quality papers as they belong in the category of high quality publications.
Stephen Garrett Siegel
Stephen Garrett Siegel also known as Steve Siegel (born January 26, 1971) is an American entrepreneur and commercial real estate investor. He is the founder and chief executive officer of The Siegel Group Nevada, Inc. He is also the founder and chief executive officer of Amazing Brands, LLC.

The Siegel Group
The Siegel Group, Inc. is an American diversified company based in Paradise, Nevada and Studio City, California.  It owns and operates hotels, hotel casinos, short-stay apartments,  office buildings, shopping centers, and land for development.
Wahkiakum County ferry
The Wahkiakum County ferry crosses the lower Columbia River between the U.S. states of Washington and Oregon, and is the last regularly scheduled car ferry to cross the Columbia River between the two states.

The ferry is located at the terminus of State Route 409, it departs from Puget Island, Washington, which the Julia Butler Hansen Bridge links to the mainland. SR 409 is a spur from State Route 4, and the ferry thus connects that highway to U.S. Route 30 in Oregon. Its status as an extension of SR 409 is why the state of Washington since 1969 has provided financial support for operation of the ferry.

As of May 2019, the ferry runs hourly (on the hour from the Washington side and 15 minutes after the hour from the Oregon side) from 5 a.m. to 10:15 p.m. 365 days a year. Lunch time service is sometimes interrupted.

Washington State Route 4
State Route 4 (SR 4) is a 62.27-mile-long (100.21 km) state highway, serving the southwestern region of the U.S. state of Washington. The highway, also known as Ocean Beach Highway, travels east along the Columbia River from U.S. Route 101 (US 101) at Johnston's Landing through Pacific, Wahkiakum and Cowlitz counties to an interchange with Interstate 5 (I-5) in Kelso. SR 4 is designated as part of the Lewis and Clark Trail Scenic Byway, a state scenic byway, as well as part of the National Highway System.

The highway, along with I-5 and SR 14, forms the former route of US 830, which ran along the Columbia River from Johnston's Landing to Maryhill from the creation of the United States Numbered Highways in 1926 until 1968. US 830 was co-signed with Primary State Highway 12 (PSH 12) from Johnston's Landing to Kelso and was created in 1937 as the successor to various unsigned state highways.
2012 Big South Conference men's soccer tournament
The 2012 Big South Conference men's soccer tournament will be the 29th edition of the tournament.  The tournament will decide the Big South Conference champion and guaranteed representative into the 2012 NCAA Division I Men's Soccer Championship. Held from November 6–11, the semifinal and championship rounds will be held at the Bryan Park Soccer Complex in Greensboro, North Carolina.

2012 NCAA Division I men's soccer tournament
The 2012 NCAA Division I men's soccer tournament is a single-elimination tournament involving 48 teams to determine the champion of the 2012 NCAA Division I men's soccer season. It was the 54th edition of the tournament. Indiana defeated Georgetown, 1–0, to win its 8th national title.
Keiji Nishioka
Dasho Keiji Nishioka (Japanese: 西岡 京治, Nishioka Keiji; 14 February 1933 – 21 March 1992) was a Japanese botanist. He was dispatched to the Kingdom of Bhutan by the Japanese Government to help modernise the Bhutanese agricultural sector. Nishioka worked in Bhutan as an agriculture expert for 28 years, from 1964 till his death in 1992. Nishioka's work helped improve the cultivation of rice and vegetables in Bhutan's Paro and Zhemgang dzongkhags (districts). He also participated in civic infrastructure development efforts in Zhemgang.

Paro District
Paro District (Dzongkha: སྤ་རོ་རྫོང་ཁག།; Wylie: Spa-ro rdzong-khag) is a district (dzongkhag), valley, river and town (population 20,000) in Bhutan. It is one of the most historic valleys in Bhutan. Both trade goods and invading Tibetans came over the pass at the head of the valley, giving Paro the closest cultural connection with Tibet of any Bhutanese district. The dominant language in Paro is Dzongkha, the national language.

The only international airport in Bhutan, Paro International Airport, is located in Paro District.
Asian Americans in Virginia
Asian Virginians make up 7% of Virginia's population, and up to at least 7.5% including those considered partially Asian. The population is at least 500,000. The largest Asian groups in Virginia are mainly Indians (South Asians), Chinese, Filipinos, Koreans, and Vietnamese (East and Southeast Asians). The state has the 8th highest percentage of Asian residents according to the 2010 Census, and is culturally connected and rooted with its Asian community.

Most of Virginia's Asian population lives in metropolitan and suburban areas of Northern Virginia, especially Arlington, Fairfax, and Loudoun counties, where Asian Americans comprise at least 10% of the total population. There is also a less populous but moderately-sized Asian population in Virginia college towns, especially Blacksburg, Charlottesville, and Williamsburg, which are at least five percent Asian. Communities are also rife in areas of Richmond, Norfolk and Virginia Beach.

Loudoun County, Virginia
Loudoun County (/ˈlaʊdən/) is in the northern part of the Commonwealth of Virginia in the United States. In 2020, the census returned a population of 420,959, making it Virginia's third-most populous county. The county seat is Leesburg. Loudoun County is part of the Washington–Arlington–Alexandria, DC–VA–MD–WV Metropolitan Statistical Area.

As of 2023, Loudoun County had a median household income of $156,821, the highest of any county or county equivalent in the nation.
Methanol economy
The methanol economy is a suggested future economy in which methanol and dimethyl ether replace fossil fuels as a means of energy storage, ground transportation fuel, and raw material for synthetic hydrocarbons and their products. It offers an alternative to the proposed hydrogen economy or ethanol economy, although these concepts are not exclusive. Methanol can be produced from a variety of sources including fossil fuels (natural gas, coal, oil shale, tar sands, etc.) as well as agricultural products and municipal waste, wood and varied biomass. It can also be made from chemical recycling of carbon dioxide.

Nobel Prize laureate George A. Olah advocated a methanol economy.

Raw material
A raw material, also known as a feedstock, unprocessed material, or primary commodity, is a basic material that is used to produce goods, finished goods, energy, or intermediate materials/Intermediate goods that are feedstock for future finished products. As feedstock, the term connotes these materials are bottleneck assets and are required to produce other products.

The term raw material denotes materials in unprocessed or minimally processed states such as raw latex, crude oil, cotton, coal, raw biomass, iron ore, plastic, air, logs, and water. The term secondary raw material denotes waste material which has been recycled and injected back into use as productive material.
Nick Wooster
Nickelson Wooster (born July 2, 1960) is an American fashion consultant who has worked with Barneys New York, Bergdorf Goodman and Neiman Marcus chain stores, as well as Calvin Klein, Polo Ralph Lauren and Thom Browne. He is best known for his street style.

Calvin Klein
Calvin Richard Klein (born November 19, 1942) is an American fashion designer. In 1968, he launched the company that later became Calvin Klein. In addition to clothing, he has also given his name to a range of perfumes, watches, and jewellery.
You Hao
You Hao (Chinese: 尤浩; pinyin: Yóu Hào; born April 26, 1992) is a Chinese artistic gymnast. He competed for the Chinese national team at the World Artistic Gymnastics Championships in 2013, 2014 and 2015. He became the World Champion on parallel bars at the 2015 World Championships.

You competed for China at the 2016 Summer Olympics.

2015 World Artistic Gymnastics Championships
The 2015 World Artistic Gymnastics Championships was the 46th edition of the Artistic Gymnastics World Championships. The competition was held from 23 October – 1 November 2015 at The SSE Hydro in Glasgow, United Kingdom, and is the first time that Scotland hosted the event. The competition served as a qualification for the 2016 Summer Olympics.

Japan won the men's team all-around competition for the first time since 1978, and the United States won the women's team all-around title for the third straight time. In the individual all-around competitions, Kōhei Uchimura and Simone Biles won their sixth and third successive title, respectively. Qualifying in thirteenth place, team Romania failed to automatically qualify to the Olympic Games for the first time since 1966.

On 4 December 2015, British Gymnastics announced that the event had been named "Sporting Event of the Year" by The Sunday Mail.
Martin L. Kersten
Martin L. Kersten (October 25, 1953 – July 6, 2022) was a computer scientist with research focus on database architectures, query optimization and their use in scientific databases. He was an architect of the MonetDB system, an open-source column store for data warehouses, online analytical processing (OLAP) and geographic information systems (GIS). He has been (co-) founder of several successful spin-offs of the Centrum Wiskunde & Informatica (CWI).

Data orientation
Data orientation is the representation of tabular data in a  linear memory model such as in-disk or in-memory. The two most common representations are column-oriented (columnar format) and row-oriented (row format).

The choice of data orientation is a trade-off and an architectural decision in databases, query engines, and numerical simulations. As a result of these tradeoffs, row-oriented formats are more commonly used in online transaction processing (OLTP) and column-oriented formats are more commonly used in online analytical processing (OLAP).

Examples of column-oriented formats include Apache ORC, Apache Parquet, Apache Arrow, formats used by BigQuery, Amazon Redshift and Snowflake. Predominant examples of row-oriented formats include CSV, formats used in most relational databases (Oracle, MySQL etc.), the in-memory format of Apache Spark, and Apache Avro.
The Wearing of the Grin
The Wearing of the Grin is a 1951 Warner Bros. Looney Tunes cartoon directed by Chuck Jones and written by Michael Maltese. The short was released on July 14, 1951, and stars Porky Pig. The title is a pun on the Irish song "The Wearing of the Green".

What's Up, Doc? (1950 film)
What's Up, Doc? is a Looney Tunes cartoon directed by Robert McKimson and produced by Warner Bros. Cartoons.  It was released by Warner Bros. Pictures on June 17, 1950, and stars Bugs Bunny and Elmer Fudd.
New York State Route 282
New York State Route 282 (NY 282) is a north–south state highway located within Tioga County in the Southern Tier of New York in the United States. It extends for 3.48 miles (5.60 km) from the Pennsylvania state line in the town of Nichols, where it connects to Pennsylvania Route 187 (PA 187), to an intersection with NY 17C in the town of Tioga. The route meets Interstate 86 (I-86) and crosses over the Susquehanna River just west of the village of Nichols.

NY 282 originally served the hamlet of Smithboro on the northern riverbank via a toll bridge when it was assigned as part of the 1930 renumbering of state highways in New York. The route south of the junction with former NY 283 was reconstructed during 1964 and 1965 while NY 282 was realigned in January 1969 to cross the river on a new bridge to the east of Smithboro as part of construction of the Southern Tier Expressway between Nichols and Owego.

Tioga, New York
Tioga is a town in Tioga County, New York, United States. The population was 4,455 at the 2020 census. The town is in the southwestern part of the county and lies between Elmira and Binghamton. Tioga is situated in the Southern Tier District of New York.
1990 Cork Senior Football Championship
The 1990 Cork Senior Football Championship was the 102nd staging of the Cork Senior Football Championship since its establishment by the Cork County Board in 1887. The draw for the opening round fixtures took place on 17 December 1989. The championship began on 20 April 1990 and ended on 4 November 1990.

Castlehaven entered the championship as the defending champions, however, they were defeated by Muskerry in the second round.

On 4 November 1990, Duhallow won the championship following an 0-08 to 0-06 defeat of St. Finbarr's in the final. This was their second championship title overall and their first title since 1936.

Colm O'Neill and Dave Barry were the championship's joint top scorers with 0-21.

1936 Cork Senior Football Championship
The 1936 Cork Senior Football Championship was the 48th staging of the Cork Senior Football Championship since its establishment by the Cork County Board in 1887.

Macroom entered the championship as the defending champions.

On 16 August 1936, Duhallow West won the championship following a 2–05 to 0–02 defeat of Clonakilty in the final at the Mardyke. This was their first ever championship title.
Prince Frederick Charles of Hesse
Frederick Charles Louis Constantine, Prince and Landgrave of Hesse (German: Friedrich Karl Ludwig Konstantin Prinz und Landgraf von Hessen-Kassel; Finnish: Fredrik Kaarle; 1 May 1868 – 28 May 1940), was the brother-in-law of the German Emperor, Wilhelm II. He was elected King of Finland on 9 October 1918, but renounced the throne on 14 December 1918.

House of Hesse
The House of Hesse is a European dynasty directly descended from the House of Reginar and Brabant. One branch ruled the region of Hesse as prince-electors until 1866, the other branch as grand dukes until 1918.
Trolls Band Together (soundtrack)
Trolls Band Together: Original Motion Picture Soundtrack is the soundtrack album to the 2023 DreamWorks Animation film Trolls Band Together, the third installment in the Trolls franchise and sequel to Trolls World Tour (2020). It was released by RCA Records, digitally on October 20, 2023, and later through physical formats on November 17, the same day as the film's release. The album was primarily produced by singer-songwriter Justin Timberlake, record producer Mike Elizondo and composer Joseph Shirley. It was promoted with two singles: "Better Place" and "It Takes Two". A separate film score album, Trolls Band Together (Original Motion Picture Score), composed by Theodore Shapiro, was released by Back Lot Music on November 10, 2023, seven days before the film's theatrical release. The song "Better Place" was nominated for a Grammy Award. The soundtrack itself won a Billboard Music Award.

Billboard Music Award for Top Soundtrack
The Billboard Music Award winners and nominees for Top Soundtrack. Notable winners include the Titanic soundtrack, High School Musical soundtrack, who was the first made for television movie or tv show soundtrack to get nominated and is the only one to have ever won that wasn't in theaters, and Frozen soundtrack, who became the first animated film soundtrack to win. The only person to win and get nominated was Celine Dion for the Titanic soundtrack. In 2017, Hamilton became the first Cast album to win. Also, in 2024, Trolls Band Together became the first non-Disney animated film soundtrack to win.