cometadata/datacite-titles-descriptions-related-identifiers huggingface dataset:
DOI: 10.3535/jvl-bet-hkf
title: Lepidoptera Linnaeus, 1758

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/f4j-568-63n
title: Amata phegea (Linnaeus, 1758)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/xbm-hhv-t93
title: Spilosoma lubricipeda (Linnaeus, 1758)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/1e9-ekh-wkb
title: Spiris striata (Linnaeus, 1758)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/9c4-ypm-d1j
title: Spilarctia lutea (Hufnagel, 1766)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/2gb-1bq-a09
title: Miltochrista miniata (Forster, 1771)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/vlq-kd7-ysq
title: Lepidoptera Linnaeus, 1758

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/wqn-hwq-9vk
title: Animalia

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/bdt-krr-jcx
title: Amata phegea (Linnaeus, 1758)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/z7q-r3k-xbh
title: Achlya flavicornis (Linnaeus, 1758)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/jwt-1fx-9hy
title: Polyploca ridens (Fabricius, 1787)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/p4j-hcw-zdn
title: Meganola albula ([Denis & Schiffermüller], 1775)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/8cz-zmm-0mh
title: Nola cucullatella (Linnaeus, 1758)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/dz4-05z-802
title: Lepidoptera Linnaeus, 1758

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/b6s-svz-b65
title: Lepidoptera Linnaeus, 1758

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/g2b-aqh-jbh
title: Pelosia muscerda (Hufnagel, 1767)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/1yb-92y-gtp
title: Achlya flavicornis (Linnaeus, 1758)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/eng-784-tws
title: Polyploca ridens (Fabricius, 1787)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/8jh-bye-13d
title: Pelosia muscerda (Hufnagel, 1767)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/sgc-kqz-9a4
title: Animalia

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/yf6-5xc-tvc
title: Katha depressa depressa (Esper, 1786)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/6z9-lgs-rte
title: Tethea (Tethea) ocularis (Linnaeus, 1767)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/fpc-872-85k
title: Lepidoptera Linnaeus, 1758

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/9gv-r58-enp
title: Cupha erymanthis nagara Fruhstorfer, 1912

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/vcv-0fe-4fg
title: Animalia

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/ggt-42c-amm
title: Animalia

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/159-ygj-xg2
title: Animalia

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/r1y-f4l-043
title: Lepidoptera Linnaeus, 1758

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/4qa-yq2-55t
title: Papilionidae

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/j6b-e53-f95
title: Leuciacria acuta Rothschild & Jordan, 1905

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/2lh-y88-9dh
title: Nola cucullatella (Linnaeus, 1758)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/j2l-cp0-r13
title: Nyea lurideola (Zincken, 1817)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/2vv-ybv-wgw
title: Nola confusalis (Herrich-Schäffer, 1847)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/yzw-hgz-h30
title: Coscinia cribraria (Linnaeus, 1758)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/mvx-nl6-jfh
title: Manulea (Manulea) complana (Linnaeus, 1758)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/zwf-hm4-7xb
title: Cilix glaucata (Scopoli, 1763)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/0gz-69n-pbr
title: Phragmatobia fuliginosa (Linnaeus, 1758)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/e5k-n2c-2bf
title: Parasemia plantaginis (Linnaeus, 1758)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/t4w-yjq-5h8
title: Lepidoptera Linnaeus, 1758

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/1p9-7wy-csf
title: Coenonympha iphis [Denis & Schiffermüller], 1776

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/x5s-ngd-b29
title: Nola holsatica Sauber, 1916

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/0xa-12k-69t
title: Delias nais Jordan, 1912

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/xdf-erj-fsk
title: Lepidoptera Linnaeus, 1758

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/rqw-2sz-xz7
title: Polyploca ridens (Fabricius, 1787)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/zxl-v7p-8dr
title: Lepidoptera Linnaeus, 1758

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.34740/kaggle/dsv/12392999
title: Billboard Hot 100 & more
DOI: 10.3535/hwa-8nr-zpd
title: Animalia

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/qzr-gx7-bxd
title: Animalia

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/lhb-1vn-hrs
title: Nola aerugula (Hübner, 1793)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/qy1-z5q-fsa
title: Achlya flavicornis (Linnaeus, 1758)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/a84-8qs-fy1
title: Cymatophorima Spuler, 1908

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/7d8-l4m-52a
title: Setina irrorella (Linnaeus, 1758)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/h25-dl5-6se
title: Atolmis rubricollis (Linnaeus, 1758)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/jbf-crz-t73
title: Phragmatobia fuliginosa (Linnaeus, 1758)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/rws-13r-zkz
title: Phragmatobia fuliginosa (Linnaeus, 1758)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/9e0-4tv-ax2
title: Katha depressa depressa (Esper, 1786)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/hat-j38-7n3
title: Indalia pygmaeola (Doubleday, 1847)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/dp8-kvx-845
title: Tethea (Tethea) ocularis (Linnaeus, 1767)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/y55-6y4-mbf
title: Lepidoptera Linnaeus, 1758

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/5v6-spq-dgm
title: Setina irrorella (Linnaeus, 1758)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/ghz-3by-lzg
title: Manulea (Manulea) complana (Linnaeus, 1758)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/y82-a9w-lgd
title: Miltochrista miniata (Forster, 1771)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/02t-jap-jbb
title: Animalia

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/bq7-mb9-fee
title: Tethea (Tethea) Ochsenheimer, 1816

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/3gn-3sm-n55
title: Animalia

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/ly0-4ll-nef
title: Meganola albula ([Denis & Schiffermüller], 1775)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/1af-r0y-tsr
title: Cilix glaucata (Scopoli, 1763)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/fly-zsc-7hh
title: Spilosoma lubricipeda (Linnaeus, 1758)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/cnr-vk3-0qt
title: Lepidoptera Linnaeus, 1758

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/c8v-yy4-0zg
title: Manulea (Manulea) complana (Linnaeus, 1758)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/t9g-p5a-xp2
title: Achlya flavicornis (Linnaeus, 1758)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/lrv-2rx-hmz
title: Lepidoptera Linnaeus, 1758

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/xmf-skq-5we
title: Miltochrista miniata miniata (Forster, 1771)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/cv1-crz-frd
title: Polyploca ridens (Fabricius, 1787)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/sa9-jyq-2hm
title: Thumatha senex (Hübner, 1804)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/9y2-jb3-axc
title: Lepidoptera Linnaeus, 1758

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/y87-60c-6yr
title: Lepidoptera Linnaeus, 1758

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/2ks-dyp-7n4
title: Animalia

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/tyk-c8w-826
title: Animalia

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/zb5-sg1-awy
title: Lepidoptera Linnaeus, 1758

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/06j-adc-aqp
title: Nola holsatica Sauber, 1916

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/p5y-nsa-k2w
title: Miltochrista miniata miniata (Forster, 1771)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/1ja-335-fbc
title: Spilarctia lutea (Hufnagel, 1766)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/dgq-hkv-7v5
title: Coscinia cribraria (Linnaeus, 1758)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/bdz-q33-rcg
title: Lepidoptera Linnaeus, 1758

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/vba-y4n-yat
title: Katha depressa depressa (Esper, 1786)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/ezl-cdv-37k
title: Katha depressa depressa (Esper, 1786)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/plh-ymz-jvv
title: Lepidoptera Linnaeus, 1758

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/ehg-02v-72w
title: Amata phegea (Linnaeus, 1758)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/twp-ax5-r16
title: Miltochrista miniata (Forster, 1771)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/s48-6ms-mg0
title: Wittia sororcula (Hufnagel, 1767)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/4wf-60e-n2p
title: Lepidoptera Linnaeus, 1758

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/v97-8w2-m01
title: Tethea (Tethea) Ochsenheimer, 1816

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/b0x-yvd-ynz
title: Spilarctia lutea (Hufnagel, 1766)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/wqm-aqx-w2s
title: Phragmatobia fuliginosa (Linnaeus, 1758)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/5w0-8ah-6s5
title: Achlya flavicornis (Linnaeus, 1758)

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.3535/feb-757-4g7
title: Animalia

description: Digital Specimen for the physical specimen hosted at Naturalis Biodiversity Center.
DOI: 10.15468/dl.ump3bb
title: Occurrence Download

description: A dataset containing 177 species occurrences available in GBIF matching the query:
{
 "and" : [
 "TaxonKey is Salvelinus fontinalis (Mitchill, 1814)",
 "Country is Italy",
 "HasCoordinate is true"
 ]
}

 The dataset includes 177 records from 7 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0100258-250525065834625/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.trqh7w
title: Occurrence Download

description: A dataset containing 8 species occurrences available in GBIF matching the query:
{
 "DatasetKey" : [
 "is (Table 1) Proportion of Toxoplasma gondii seropositive arctic foxes (Alopex lagopus) by age group and geographic area"
 ]
}

 The dataset includes 8 records from 1 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0004171-160311141623029/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.vsszmi
title: Occurrence Download

description: A dataset containing 32 species occurrences available in GBIF matching the query:
{
 "DatasetKey" : [
 "is (Table 1) Proportion of Toxoplasma gondii seropositive arctic foxes (Alopex lagopus) by age group and geographic area"
 ]
}

 The dataset includes 32 records from 1 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0026445-190415153152247/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.r4zyrb
title: Occurrence Download

description: A dataset containing 8 species occurrences available in GBIF matching the query:
{
 "DatasetKey" : [
 "is (Table 1) Proportion of Toxoplasma gondii seropositive arctic foxes (Alopex lagopus) by age group and geographic area"
 ]
}

 The dataset includes 8 records from 1 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0004969-171219132708484/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.e8wqq9
title: Occurrence Download

description: A dataset containing 4579 species occurrences available in GBIF matching the query:
{
 "DatasetKey" : [
 "is Estación Biológica de Doñana - CSIC, Anfibios"
 ]
}

 The dataset includes 4579 records from 1 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0412689-210914110416597/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.xptza6
title: Occurrence Download

description: A dataset containing 142322473 species occurrences available in GBIF matching the query:
{
 "and" : [
 "Geometry POLYGON((-120.6008 34.77855,-103.38106 32.06459,-103.38106 48.36944,-124.5333 48.36944,-124.56125 41.52126,-120.6008 34.77855))",
 "HasGeospatialIssue is false"
 ]
}

 The dataset includes 142322473 records from 1456 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0010989-220831081235567/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.qmeh25
title: Occurrence Download

description: A dataset containing 8 species occurrences available in GBIF matching the query:
{
 "DatasetKey" : [
 "is (Table 1) Proportion of Toxoplasma gondii seropositive arctic foxes (Alopex lagopus) by age group and geographic area"
 ]
}

 The dataset includes 8 records from 1 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0009557-171124123535762/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.bwg7qy
title: Occurrence Download

description: A dataset containing 166201469 species occurrences available in GBIF matching the query:
{
 "BasisOfRecord" : [
 "is Specimen"
 ]
}

 The dataset includes 166201469 records from 10765 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0030213-190415153152247/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.17632/zhm6t5vdpm
title: Supplementary materials for Ph.D. thesis "AI Digital Twin of Roll-to-Roll Printing System for Autonomous Manufacturing"

description: The supplementary materials demonstrate the autonomous Bayesian optimization of a proportional-integral (PI) web tension controller through a Digital Twin (DT) of a roll-to-roll (R2R) manufacturing system. The operation is conducted on the DT computer, which communicates with the Physical Twin (PT), i.e., the R2R manufacturing system, via the OPC UA protocol and the web tension step response is displayed using DT operation module. Additionally the step response file is collected via SFTP communication. In each iteration, the Bayesian optimization algorithm suggests new values for the proportional (Kp) and integral (Ki) controller gains based on the results of previous experiments. The step response data is then processed to extract key dynamic control characteristics, including time constant, overshoot, and settling time. These characteristics are combined into a quality score as a weighted sum, which is used in Gaussian process modeling. The updated model is subsequently used to query new Kp and Ki gains through the Expected Improvement acquisition function. This real-time communication and model updating optimize the control of the R2R system. The video playback speed of the Supplementary video S1 is increased by a factor of 10.
DOI: 10.5281/zenodo.14583701
title: 전이성

description: 오일러 피 함수에서 다음이 성립한다.

 

a의 phi(n)≡1, (mod n)

 

a와 n은 서로소

 

(a의 phi(n)-1)/n=1

 

 

a의 phi(n)=n+1

 

logan+1=phi(n)

 

n에 따른 a값이 있으면 phi(n)의 값을 계산할 수 있다.

 

phi(n)의 정의상 n과 서로소인 n이하의 수이므로 값이 phi(n)이 n보다 작아야 하므로

 

logan+1<n

 

a의 n보다 작은 수 제곱은 n+1과 같다.

 

a=log(n+1)/(n-x)

log(n+1)/(n-x)≠n, log(n+1)/(n-x)=phi(h), n=phi(h), (n-x)=phi(n)을 연립해서 풀면 된다.

 

 

Phi(n)=f(n), phi(h)를 f(h)로 표현한다.

 

log(n+1)/(n-x)≠n, log(n+1)/(n-x)=f(h), n=f(h), (n-x)=f(n)

 

f(n)=?

 

 

f(n) = \frac{\log(n+1)}{n-x}, \quad x \neq \frac{n^2 - \log(n+1)}{n}.

 

1<=x<n x는 n, x는 자연수

 

 

f(n) = \frac{\log(n+1)}{(n - x) + k \cdot \log(n+1) - (n - x)} = \frac{\log(n+1)}{k \cdot \log(n+1)} = \frac{1}{k}

\epsilon = k \cdot \log(n+1) - (n - x)

 

S(k) = \sum_{x=x_1}^{x_k} \frac{1}{k}.

 

 

f(n) = \sum_{k=1}^{n} \left(k + \frac{\log(k+1)}{k}\right).

 

 

주어진 수식에 n=30 x는 1부터 29까지의 수를 넣으면 답이 나온다.

 

 

https://chatgpt.com/share/67744030-67d8-800c-a41c-9ca193ab404b
DOI: 10.5281/zenodo.14583702
title: 전이성

description: 오일러 피 함수에서 다음이 성립한다.

 

a의 phi(n)≡1, (mod n)

 

a와 n은 서로소

 

(a의 phi(n)-1)/n=1

 

 

a의 phi(n)=n+1

 

logan+1=phi(n)

 

n에 따른 a값이 있으면 phi(n)의 값을 계산할 수 있다.

 

phi(n)의 정의상 n과 서로소인 n이하의 수이므로 값이 phi(n)이 n보다 작아야 하므로

 

logan+1<n

 

a의 n보다 작은 수 제곱은 n+1과 같다.

 

a=log(n+1)/(n-x)

log(n+1)/(n-x)≠n, log(n+1)/(n-x)=phi(h), n=phi(h), (n-x)=phi(n)을 연립해서 풀면 된다.

 

 

Phi(n)=f(n), phi(h)를 f(h)로 표현한다.

 

log(n+1)/(n-x)≠n, log(n+1)/(n-x)=f(h), n=f(h), (n-x)=f(n)

 

f(n)=?

 

 

f(n) = \frac{\log(n+1)}{n-x}, \quad x \neq \frac{n^2 - \log(n+1)}{n}.

 

1<=x<n x는 n, x는 자연수

 

 

f(n) = \frac{\log(n+1)}{(n - x) + k \cdot \log(n+1) - (n - x)} = \frac{\log(n+1)}{k \cdot \log(n+1)} = \frac{1}{k}

\epsilon = k \cdot \log(n+1) - (n - x)

 

S(k) = \sum_{x=x_1}^{x_k} \frac{1}{k}.

 

 

f(n) = \sum_{k=1}^{n} \left(k + \frac{\log(k+1)}{k}\right).

 

 

주어진 수식에 n=30 x는 1부터 29까지의 수를 넣으면 답이 나온다.

 

 

https://chatgpt.com/share/67744030-67d8-800c-a41c-9ca193ab404b
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