1
{{NumberPageLink|prev = 0|next = 2}} == Number == $1$ ('''one''') is: :The immediate successor element of zero in the set of natural numbers $\N$ :The only (strictly) positive integer which is neither prime nor composite :The only (strictly) positive integer which is a divisor of every integer === $0$th Term === :The $0$th (zeroth) power of every non-non-zero number: ::$\forall n: n \ne 0 \implies n^1 = 1$ :The $0$th term of Göbel's sequence, by definition :The $0$th term of the $3$-Göbel sequence, by definition :The $0$th and $1$st Catalan numbers: ::$1 = \dfrac 1 {0 + 1} \dbinom {2 \times 0} 1 = \dfrac 1 1 \times 1$ ::$1 = \dfrac 1 {1 + 1} \dbinom {2 \times 1} 1 = \dfrac 1 2 \times 2$ :The $0$th and $1$st Bell numbers === $1$st Term === :The $1$st (strictly) positive integer :The $1$st (strictly) positive integer :The $1$st (positive) odd number ::$1 = 0 \times 2 + 1$ :The $1$st number to be both square and triangular: ::$1 = 1^2 = \dfrac {1 \times \paren {1 + 1}} 2$ :The $1$st square number to be the $\sigma$ (sigma) value of some (strictly) positive integer: ::$1 = \map \sigma 1$ :The $1$st generalized pentagonal number: ::$1 = \dfrac {1 \paren {3 \times 1 - 1} } 2$ :The $1$st highly composite number: ::$\map \tau 1 = 1$ :The $1$st special highly composite number :The $1$st highly abundant number: ::$\map \sigma 1 = 1$ :The $1$st superabundant number: ::$\dfrac {\map \sigma 1} 1 = \dfrac 1 1 = 1$ :The $1$st almost perfect number: ::$\map \sigma 1 = 1 = 2 - 1$ :The $1$st factorial: ::$1 = 1!$ :The $1$st superfactorial: ::$1 = 1\$ = 1!$ :The $1$st Lucas number after the zeroth $(2)$ :The $1$st Ulam number :The $1$st (strictly) positive integer which cannot be expressed as the sum of exactly $5$ non-zero squares :The $1$st of the $24$ positive integers which cannot be expressed as the sum of distinct non-pythagorean primes :The $1$st of the $5$ known powers of $2$ whose digits are also all powers of $2$ :The $1$st factorion base $10$: ::$1 = 1!$ :The $1$st of the trivial $1$-digit pluperfect digital invariants: ::$1^1 = 1$ :The $1$st of the $1$st pair of consecutive integers whose product is a primorial: ::$1 \times 2 = 2 = 2 \#$ :The $1$st of the (trivial $1$-digit) Zuckerman numbers: ::$1 = 1 \times 1$ :The $1$st of the (trivial $1$-digit) harshad numbers: ::$1 = 1 \times 1$ :The $1$st positive integer whose cube is palindromic (in this case trivially): ::$1^3 = 1$ :The $1$st lucky number :The $1$st palindromic lucky number :The $1$st Stern number :The $1$st Cullen number: ::$1 = 0 \times 2^0 + 1$ :The $1$st number whose $\sigma$ value is square: ::$\map \sigma 1 = 1 = 1^2$ :The $1$st positive integer after $1$ of which the product of its Euler $\phi$ function and its $\tau$ function equals its $\sigma$ function: ::$\map \phi 1 \map \tau 1 = 1 \times 1 = 1 = \map \sigma 1$ :The $1$st positive integer solution to $\map \phi n = \map \phi {n + 1}$: ::$\map \phi 1 = 1 = \map \phi 2$ :The $1$st element of the Fermat set :The $1$st integer $n$ with the property that $\map \tau n \divides \map \phi n \divides \map \sigma n$: ::$\map \tau 1 = 1$, $\map \phi 1 = 1$, $\map \sigma 1 = 1$ :The $1$st Lucas number which is also triangular :The $1$st tetrahedral number: ::$1 = \dfrac {1 \left({1 + 1}\right) \left({1 + 2}\right)} 6$ :The $1$st of the $3$ tetrahedral numbers which are also square :The $1$st trimorphic number: ::$1^3 = \mathbf 1$ :The $1$st powerful number (vacuously) :The $1$st integer which equals the number of digits in its factorial: ::$1! = 1$ :which has $1$ digit :The $1$st power of $2$ which is the sum of distinct powers of $3$: ::$1 = 2^0 = 3^0$ :The $1$st square which has no more than $2$ distinct digits :The $1$st pentagonal number: ::$1 = \dfrac {1 \left({1 \times 3 - 1}\right)} 2$ :The $1$st pentagonal number which is also palindromic: ::$1 = \dfrac {1 \left({1 \times 3 - 1}\right)} 2$ :The $1$st square pyramidal number: ::$1 = \dfrac {1 \paren {1 + 1} \paren {2 \times 1 + 1} } 6$ :The $1$st pentatope number: ::$1 = \dfrac {1 \paren {1 + 1} \paren {1 + 2} \paren {1 + 3} } {24}$ :The $1$st automorphic number: ::$1^2 = \mathbf 1$ :The $1$st number such that $2 n^2 - 1$ is square: ::$2 \times 1^2 - 1 = 2 \times 1 - 1 = 1 = 1^2$ {{WIP|Find out what sequence this belongs to, because it has not been set up on the $5$ page}} :The $1$st Ore number: ::$\dfrac {1 \times \map \tau 1} {\map \sigma 1} = 1$ :and the $1$st whose divisors also have an arithmetic mean which is an integer: ::$\dfrac {\map \sigma 1} {\map \tau 1} = 1$ :The $1$st hexagonal number: ::$1 = 1 \paren {2 \times 1 - 1}$ :The $1$st pentagonal pyramidal number: ::$1 = \dfrac {1^2 \paren {1 + 1} } 2$ :The $1$st heptagonal number: ::$1 = \dfrac {1 \paren {5 \times 1 - 3} } 2$ :The $1$st centered hexagonal number: ::$1 = 1^3 - 0^3$ :The $1$st hexagonal pyramidal number: :The $1$st Woodall number: ::$1 = 1 \times 2^1 - 1$ :The $1$st happy number: ::$1 \to 1^2 = 1$ :The $1$st positive integer the sum of whose divisors is a cube: ::$\map \sigma 1 = 1 = 1^3$ :The $1$st cube number: ::$1 = 1^3$ :The $1$st of the only two cubic Fibonacci numbers :The $1$st octagonal number: ::$1 = 1 \paren {3 \times 1 - 2}$ :The $1$st heptagonal pyramidal number: ::$1 = \dfrac {1 \paren {1 + 1} \paren {5 \times 1 - 2} } 6$ :The $1$st Kaprekar triple: ::$1^3 = 1 \to 0 + 0 + 1 = 1$ :The $1$st palindromic cube: ::$1 = 1^3$ :The $1$st Kaprekar number: ::$1^2 = 01 \to 0 + 1 = 1$ :The $1$st number whose square has a $\sigma$ value which is itself square: ::$\map \sigma 1 = 1 = 1^2$ :The $1$st of the $5$ tetrahedral numbers which are also triangular :The $1$st positive integer which cannot be expressed as the sum of a square and a prime :The $1$st positive integer such that all smaller positive integers coprime to it are prime :The (trivial) $1$st repunit :The $1$st fourth power: ::$1 = 1 \times 1 \times 1 \times 1$ :The $1$st integer $m$ whose cube can be expressed (trivially) as the sum of $m$ consecutive squares: ::$1^3 = \displaystyle \sum_{k \mathop = 1}^1 \left({0 + k}\right)^2$ :The $1$st and $2$nd Fibonacci numbers after the zeroth ($0$): ::$1 = 0 + 1$ :The $1$st positive integer whose $\sigma$ value of its Euler $\phi$ value equals its $\sigma$ value: ::$\map \sigma {\map \phi 1} = \map \sigma 1 = 1 = \map \sigma 1$ :The $1$st square pyramorphic number: ::$1 = \displaystyle \sum_{k \mathop = 1}^1 k^2 = \dfrac {1 \paren {1 + 1} \paren {2 \times 1 + 1} } 6$ :The $1$st of the $4$ square pyramidal numbers which are also triangular :The $1$st Wonderful Demlo number :The $1$st obstinate number :The index of the $1$st Cullen prime: ::$1 \times 2^1 + 1 = 3$ :The index of the $1$st Mersenne number which {{AuthorRef|Marin Mersenne}} asserted to be prime ::($1$ itself was classified as a prime number in those days) :The number of different representations of $1$ as the sum of $1$ unit fractions (degenerate case) :The $1$st centered hexagonal number which is also square :The $1$st pentagonal number which is also triangular: ::$1 = \dfrac {1 \paren {3 \times 1 - 1} } 2 = \dfrac {1 \times \paren {1 + 1} } 2$ :The $1$st odd positive integer that cannot be expressed as the sum of exactly $4$ distinct non-zero square numbers all of which are coprime :The $1$st odd number which cannot be expressed as the sum of an integer power and a prime number :The number of distinct free monominoes === $2$nd Term === :The $2$nd after $0$ of the $5$ Fibonacci numbers which are also triangular :The $2$nd palindromic triangular number after $0$ :The $2$nd integer $n$ after $0$ such that $2^n$ contains no zero in its decimal representation: ::$2^1 = 2$ :The $2$nd integer $n$ after $0$ such that $5^n$ contains no zero in its decimal representation: ::$5^1 = 5$ :The $2$nd integer $n$ after $0$ such that both $2^n$ and $5^n$ have no zeroes: ::$2^1 = 2, 5^1 = 5$ :The $2$nd palindromic integer which is the index of a palindromic triangular number after $0$: ::$T_1 = 1$ :The $1$st palindromic integer after $0$ whose square is also palindromic integer ::$1^2 = 1$ :The $2$nd Dudeney number after $0$: ::$1^3 = 1$ :The $2$nd number after $0$ which is (trivially) the sum of the increasing powers of its digits taken in order: ::$1^1 = 1$ :The $2$nd non-negative integer $n$ after $0$ such that the Fibonacci number $F_n$ ends in $n$ :The $2$nd after $0$ of the $3$ Fibonacci numbers which equals its index :The $2$nd subfactorial after $0$: ::$1 = 2! \paren {1 - \dfrac 1 {1!} + \dfrac 1 {2!} }$ :The $2$nd integer $m$ after $0$ such that $m^2 = \dbinom n 0 + \dbinom n 1 + \dbinom n 2 + \dbinom n 3$ for integer $n$: ::$1^2 = \dbinom 0 0 + \dbinom 0 1 + \dbinom 0 2 + \dbinom 0 3$ :The $2$nd integer $m$ after $0$ such that $m! + 1$ (its factorial plus $1$) is prime: ::$1! + 1 = 1 + 1 = 2$ :The $2$nd integer after $0$ such that its  double factorial plus $1$ is prime: ::$1!! + 1 = 2$ :The $2$nd integer after $0$ which is palindromic in both decimal and binary: ::$1_{10} = 1_2$ :The $2$nd integer after $0$ which is palindromic in both decimal and ternary: ::$1_{10} = 1_3$ :The $2$nd Ramanujan-Nagell number after $0$: ::$1 = 2^1 - 1 = \dfrac {1 \left({1 + 1}\right)} 2$ :The number of different representations of $1$ as the sum of $2$ unit fractions: ::$1 = \dfrac 1 2 + \dfrac 1 2$ :The number of distinct free dominoes === Miscellaneous === :The total of all the entries in the trivial magic square of order $1$: ::$1 = \displaystyle \sum_{k \mathop = 1}^{1^2} k = \dfrac {1^2 \paren {1^2 + 1} } 2$ :The total of all the entries in the trivial magic cube of order $1$: ::$1 = \displaystyle \sum_{k \mathop = 1}^{1^3} k = \dfrac {1^3 \paren {1^3 + 1} } 2$ :The magic constant of the trivial magic square of order $1$: ::$1 = \displaystyle \dfrac 1 1 \sum_{k \mathop = 1}^{1^2} k = \dfrac {1 \paren {1^2 + 1} } 2$ :The magic constant of the trivial magic cube of order $1$: ::$1 = \displaystyle \dfrac 1 {1^2} \sum_{k \mathop = 1}^{1^3} k = \dfrac {1 \paren {1^3 + 1} } 2$ {{ArithmeticFunctionTable|n = 1|tau = 1|phi = 1|sigma = 1}} == Also see == * Definition:Unity * One is not Prime * Divisors of One * One Divides all Integers === Previous in sequence: $0$ === ==== Next in sequence: $2$ ==== * {{NumberPageLink|prev = 0|next = 2|type = Subfactorial|cat = Subfactorials}} * {{NumberPageLink|prev = 0|next = 2|result = Sequence of Integers whose Factorial plus 1 is Prime}} * {{NumberPageLink|prev = 0|next = 2|result = Prime Values of Double Factorial plus 1}} * {{NumberPageLink|prev = 0|next = 2|type = Fibonacci Number|cat = Fibonacci Numbers}} * {{NumberPageLink|prev = 0|next = 2|result = Powers of 2 with no Zero in Decimal Representation}} * {{NumberPageLink|prev = 0|next = 2|result = Powers of 5 with no Zero in Decimal Representation}} * {{NumberPageLink|prev = 0|next = 2|result = Powers of 2 and 5 without Zeroes}} * {{NumberPageLink|prev = 0|next = 2|result = Palindromes in Base 10 and Base 3}} * {{NumberPageLink|prev = 0|next = 2|result = Numbers which are Sum of Increasing Powers of Digits}} * {{NumberPageLink|prev = 0|next = 2|result = Square Formed from Sum of 4 Consecutive Binomial Coefficients}} * {{NumberPageLink|prev = 0|next = 2|result = Palindromic Indices of Palindromic Triangular Numbers}} * {{NumberPageLink|prev = 0|next = 2|result = Square of Small-Digit Palindromic Number is Palindromic}} ==== Next in sequence: $3$ ==== * {{NumberPageLink|prev = 0|next = 3|type = Triangular Number|cat = Triangular Numbers}} * {{NumberPageLink|prev = 0|next = 3|result = Palindromes in Base 10 and Base 2}} * {{NumberPageLink|prev = 0|next = 3|result = Triangular Fibonacci Numbers}} * {{NumberPageLink|prev = 0|next = 3|result = Palindromic Triangular Numbers}} * {{NumberPageLink|prev = 0|next = 3|type = Ramanujan-Nagell Number|cat = Ramanujan-Nagell Numbers}} ==== Next in sequence: $5$ ==== * {{NumberPageLink|prev = 0|next = 5|result = Fibonacci Numbers which equal their Index}} * {{NumberPageLink|prev = 0|next = 5|result = Sequence of Fibonacci Numbers ending in Index}} ==== Next in sequence: $8$ ==== * {{NumberPageLink|prev = 0|next = 8|type = Dudeney Number|cat = Dudeney Numbers}} === Previous in sequence: $2$ === * {{NumberPageLink|prev = 2|next = 3|type = Lucas Number|cat = Lucas Numbers}} === Next in sequence: $2$ === * {{NumberPageLink|next = 2|type = Generalized Pentagonal Number|cat = Generalized Pentagonal Numbers}} * {{NumberPageLink|next = 2|type = Highly Composite Number|cat = Highly Composite Numbers}} * {{NumberPageLink|next = 2|type = Special Highly Composite Number|cat = Special Highly Composite Numbers}} * {{NumberPageLink|next = 2|type = Highly Abundant Number|cat = Highly Abundant Numbers}} * {{NumberPageLink|next = 2|type = Superabundant Number|cat = Superabundant Numbers}} * {{NumberPageLink|next = 2|type = Almost Perfect Number|cat = Almost Perfect Numbers}} * {{NumberPageLink|next = 2|type = Factorial|cat = Factorials}} * {{NumberPageLink|next = 2|type = Superfactorial|cat = Superfactorials}} * {{NumberPageLink|next = 2|type = Fibonacci Number|cat = Fibonacci Numbers}} * {{NumberPageLink|next = 2|type = Catalan Number|cat = Catalan Numbers}} * {{NumberPageLink|next = 2|type = Ulam Number|cat = Ulam Numbers}} * {{NumberPageLink|next = 2|result = Sequence of Powers of 2|cat = Powers of 2}} * {{NumberPageLink|next = 2|result = Powers of 2 with no Zero in Decimal Representation}} * {{NumberPageLink|next = 2|result = Powers of 2 and 5 without Zeroes}} * {{NumberPageLink|next = 2|result = Integer not Expressible as Sum of 5 Non-Zero Squares}} * {{NumberPageLink|next = 2|result = Integers such that all Coprime and Less are Prime}} * {{NumberPageLink|next = 2|type = Göbel's Sequence|cat = Göbel's Sequence}} * {{NumberPageLink|next = 2|type = 3-Göbel Sequence|cat = Göbel's Sequence}} * {{NumberPageLink|next = 2|result = Positive Integers Not Expressible as Sum of Distinct Non-Pythagorean Primes}} * {{NumberPageLink|next = 2|result = Powers of 2 whose Digits are Powers of 2}} * {{NumberPageLink|next = 2|type = Pluperfect Digital Invariant|cat = Pluperfect Digital Invariants}} * {{NumberPageLink|next = 2|result = Factorions Base 10|cat = Factorions}} * {{NumberPageLink|next = 2|result = Consecutive Integers whose Product is Primorial}} * {{NumberPageLink|next = 2|type = Zuckerman Number|cat = Zuckerman Numbers}} * {{NumberPageLink|next = 2|type = Harshad Number|cat = Harshad Numbers}} * {{NumberPageLink|next = 2|result = Square Formed from Sum of 4 Consecutive Binomial Coefficients}} * {{NumberPageLink|next = 2|type = Bell Number|cat = Bell Numbers}} * {{NumberPageLink|next = 2|result = Sequence of Integers whose Cube is Palindromic}} * {{NumberPageLink|next = 2|result = Number of Free Polyominoes}} * {{NumberPageLink|next = 2|type = Mersenne Prime/Historical Note|cat = Mersenne's Assertion}} === Next in sequence: $3$ === * {{NumberPageLink|next = 3|result = Sequence of Powers of 3|cat = Powers of 3}} * {{NumberPageLink|next = 3|type = Lucky Number|cat = Lucky Numbers}} * {{NumberPageLink|next = 3|result = Sequence of Palindromic Lucky Numbers}} * {{NumberPageLink|next = 3|type = Stern Number|cat = Stern Numbers}} * {{NumberPageLink|next = 3|type = Cullen Number|cat = Cullen Numbers}} * {{NumberPageLink|next = 3|result = Numbers whose Sigma is Square|cat = Numbers whose Sigma is Square}} * {{NumberPageLink|next = 3||result = Integers whose Phi times Tau equal Sigma}} * {{NumberPageLink|next = 3|result = Consecutive Integers with Same Euler Phi Value}} * {{NumberPageLink|next = 3|type = Fermat Set}} * {{NumberPageLink|next = 3|result = Numbers such that Tau divides Phi divides Sigma}} * {{NumberPageLink|next = 3|result = Triangular Lucas Numbers}} * {{NumberPageLink|next = 3|result = Representation of 1 as Sum of n Unit Fractions}} * {{NumberPageLink|next = 3|result = Odd Numbers Not Expressible as Sum of 4 Distinct Non-Zero Coprime Squares}} === Next in sequence: $4$ === * {{NumberPageLink|next = 4|result = Sequence of Powers of 4|cat = Powers of 4}} * {{NumberPageLink|next = 4|type = Tetrahedral Number|cat = Tetrahedral Numbers}} * {{NumberPageLink|next = 4|result = Square and Tetrahedral Numbers}} * {{NumberPageLink|next = 4|type = Trimorphic Number|cat = Trimorphic Numbers}} * {{NumberPageLink|next = 4|type = Powerful Number|cat = Powerful Numbers}} * {{NumberPageLink|next = 4|result = Powers of 2 which are Sum of Distinct Powers of 3}} * {{NumberPageLink|next = 4|result = Squares with No More than 2 Distinct Digits}} === Next in sequence: $5$ === * {{NumberPageLink|next = 5|result = Sequence of Powers of 5|cat = Powers of 5}} * {{NumberPageLink|next = 5|type = Pentagonal Number|cat = Pentagonal Numbers}} * {{NumberPageLink|next = 5|result = Sequence of Palindromic Pentagonal Numbers}} * {{NumberPageLink|next = 5|type = Square Pyramidal Number|cat = Pyramidal Numbers}} * {{NumberPageLink|next = 5|type = Pentatope Number|cat = Pentatope Numbers}} * {{NumberPageLink|next = 5|type = Automorphic Number|cat = Automorphic Numbers}} * {{NumberPageLink|next = 5|result = Magic Constant of Magic Square}} * {{NumberPageLink|next = 5|result = Odd Numbers not Sum of Prime and Power}} === Next in sequence: $6$ === * {{NumberPageLink|next = 6|result = Sequence of Powers of 6|cat = Powers of 6}} * {{NumberPageLink|next = 6|type = Ore Number|cat = Ore Numbers}} * {{NumberPageLink|next = 6|result = Sequence of Numbers with Integer Arithmetic and Harmonic Means of Divisors}} * {{NumberPageLink|next = 6|type = Hexagonal Number|cat = Hexagonal Numbers}} * {{NumberPageLink|next = 6|type = Pentagonal Pyramidal Number|cat = Pyramidal Numbers}} === Next in sequence: $7$ === * {{NumberPageLink|next = 7|cat = Powers of 7|result = Sequence of Powers of 7}} * {{NumberPageLink|next = 7|type = Centered Hexagonal Number|cat = Centered Hexagonal Numbers}} * {{NumberPageLink|next = 7|type = Hexagonal Pyramidal Number|cat = Pyramidal Numbers}} * {{NumberPageLink|next = 7|type = Heptagonal Number|cat = Heptagonal Numbers}} * {{NumberPageLink|next = 7|type = Woodall Number|cat = Woodall Numbers}} * {{NumberPageLink|next = 7|type = Happy Number|cat = Happy Numbers}} * {{NumberPageLink|next = 7|result = Integers whose Sigma Value is Cube}} === Next in sequence: $8$ === * {{NumberPageLink|next = 8|result = Sequence of Powers of 8|cat = Powers of 8}} * {{NumberPageLink|next = 8|type = Cube Number|cat = Cube Numbers}} * {{NumberPageLink|next = 8|result = Cubic Fibonacci Numbers}} * {{NumberPageLink|next = 8|type = Octagonal Number|cat = Octagonal Numbers}} * {{NumberPageLink|next = 8|type = Heptagonal Pyramidal Number|cat = Pyramidal Numbers}} * {{NumberPageLink|next = 8|type = Kaprekar Triple|cat = Kaprekar Numbers}} * {{NumberPageLink|next = 8|result = Sequence of Palindromic Cubes}} === Next in sequence: $9$ === * {{NumberPageLink|next = 9|result = Sequence of Powers of 9|cat = Powers of 9}} * {{NumberPageLink|next = 9|type = Kaprekar Number|cat = Kaprekar Numbers}} * {{NumberPageLink|next = 9|result = Square Numbers whose Sigma is Square|cat = Square Numbers whose Sigma is Square}} * {{NumberPageLink|next = 9|result = Magic Constant of Magic Cube}} === Next in sequence: $10$ === * {{NumberPageLink|next = 10|result = Sum of Terms of Magic Square}} * {{NumberPageLink|next = 10|cat = Powers of 10|result = Sequence of Powers of 10}} * {{NumberPageLink|next = 10|result = Tetrahedral and Triangular Numbers}} * {{NumberPageLink|next = 10|result = Numbers not Sum of Square and Prime}} === Next in sequence: $11$ === * {{NumberPageLink|next = 11|result = Sequence of Powers of 11|cat = Powers of 11}} * {{NumberPageLink|next = 11|type = Repunit|cat = Repunits}} === Next in sequence: $12$ and above === * {{NumberPageLink|next = 12|result = Sequence of Powers of 12|cat = Powers of 12}} * {{NumberPageLink|next = 13|result = Sequence of Powers of 13|cat = Powers of 13}} * {{NumberPageLink|next = 14|result = Sequence of Powers of 14|cat = Powers of 14}} * {{NumberPageLink|next = 15|result = Sequence of Powers of 15|cat = Powers of 15}} * {{NumberPageLink|next = 16|type = Fourth Power|cat = Fourth Powers}} * {{NumberPageLink|next = 16|result = Sequence of Powers of 16|cat = Powers of 16}} * {{NumberPageLink|next = 22|result = Numbers Equal to Number of Digits in Factorial}} * {{NumberPageLink|next = 36|result = Integer both Square and Triangular}} * {{NumberPageLink|next = 36|result = Sum of Terms of Magic Cube}} * {{NumberPageLink|next = 47|result = Numbers whose Cube equals Sum of Sequence of that many Squares|cat = Numbers whose Cube equals Sum of Sequence of that many Squares}} * {{NumberPageLink|next = 55|result = Square Pyramidal and Triangular Numbers}} * {{NumberPageLink|next = 55|type = Square Pyramorphic Number|cat = Square Pyramorphic Numbers}} * {{NumberPageLink|next = 87|result = Integers for which Sigma of Phi equals Sigma}} * {{NumberPageLink|next = 121|type = Wonderful Demlo Number|cat = Wonderful Demlo Numbers}} * {{NumberPageLink|next = 127|type = Obstinate Number|cat = Obstinate Numbers}} * {{NumberPageLink|next = 141|type = Cullen Prime|cat = Cullen Primes}} * {{NumberPageLink|next = 169|result = Sequence of Square Centered Hexagonal Numbers}} * {{NumberPageLink|next = 210|result = Triangular Numbers which are also Pentagonal}} == Historical Note == {{:1/Historical Note}} == Linguistic Note == {{:1/Linguistic Note}} == Sources == * {{BookReference|Les Nombres Remarquables|1983|François Le Lionnais|author2 = Jean Brette|prev = Integral from 0 to 1 of Complete Elliptic Integral of First Kind|next = Trivial Group is Smallest Group}}: $1$ * {{BookReference|The Penguin Dictionary of Mathematics|1998|David Nelson|ed = 2nd|edpage = Second Edition|prev = Definition:Unit Vector|next = Definition:Universal Quantifier|entry = unity}} * {{BookReference|The Penguin Dictionary of Mathematics|2008|David Nelson|ed = 4th|edpage = Fourth Edition|prev = Definition:Unit Vector|next = Universal Instantiation|entry = unity}} * {{BookReference|The Concise Oxford Dictionary of Mathematics|2014|Christopher Clapham|author2 = James Nicholson|ed = 5th|edpage = Fifth Edition|prev = Definition:Unit Vector|next = Definition:Universal Gravitational Constant|entry = unity}}