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Euler totient function \(\phi(n)\): count numbers \(1 \le k \le n\) such that \(k\) is coprime with (n), i.e., A000010.

The prime numbers, i.e., A000040.

Tetranacci numbers, i.e., A000078.

Euler up/down numbers: e.g.f. \(\sec(x) + \tan(x)\), i.e. A000111.

Binary weight, i.e., A000120.

Tangent (or "Zag") numbers: e.g.f. \(\tan(x)\), also (up to signs), e.g., \(\tanh(x)\), i.e., A000182.

The sum of the divisors of \(n\), i.e., A000203.

Triangular numbers: \(T_{n} = \frac{n(n+1)}{2}\), i.e., A000217.

Pseudo-Fibonacci numbers, i.e., A000285.

The squares: \(a000290(n) = n^2\), i.e., A000290.

\(a(n) = n^n\), i.e., A000312.

Pentagonal numbers: \(P_{n} = \frac{n(3n-1)}{2}\), i.e., A000326.

Square pyramidal numbers: \(a(n) = 0^2+1^2+2^2 + \dotsb + n^2 = \frac{n(n+1)(2n+1)}{6}\), i.e., A000330.

Euler (or secant or "Zig") numbers: e.g.f. (even powers only) \(\sec(x) = \frac{1}{\cos(x)}\), i.e., A000364.

Hexagonal numbers: \(H_{n} = n(2n-1)\), i.e., A000384.

Sum of first \(n\) cubes; or \(n\)-th triangular number squared, i.e. A000537.

Aliquot sum of \(n\), i.e., A001065.

Products of rows of Pascal's triangle, i.e., A001142.

Full reptend primes, i.e., A001913.

Kempner numbers: smallest positive integer \(m\) such that \(n\) divides \(m!\), i.e., A002034.

Summatory totient, i.e., A002088.

See also a000010.

Hyperfactorials: \(\prod_{k=1}^n k^k\), i.e. A002109.

See also a000312.

Multiplicative order of \(2 \bmod{2n + 1}\), i.e., A002326.

Oblong (or promic, pronic, or heteromecic) numbers: \(a002378(n) = n(n+1)\), i.e., A002378.

Length of shortest addition chain for \(n\), i.e. A003313.

Sort the digits of \(n\) in ascending order, removing any zeros, i.e., A004185.

Abundant numbers (sum of divisors of \(n\) exceeds \(2n\), i.e. A005101.

\(a(n) = \sum_{k=0}^{\lfloor \frac{n}{4} \rfloor} \binom{n-2k}{2k}\), i.e., A005252.

Pascal's triangle read by rows: \(\binom{n}{k}\) for \(0 \le k \le n\), i.e., A007318.

Largest squarefree number diving \(n\): the square free kernel of \(n\), \(\text{rad}(n)\), radical of \(n\), i.e., A007947.

Digital sum of \(n\), i.e., A007953.

Number of (positive) squarefree numbers \(< n\), i.e., A013928.

\(a(n) = -1 + \Phi(n)\), i.e., A015614.

See also a002088.

Irregular triangle in which first row is \(1\), \(n\)-th row \((n > 1)\) lists distinct prime factors of \(n\), i.e. A027748.

See distinctPrimeFactors.

Numbers that are sums of consecutive squares, i.e. A034705.

See also a000290 and squares.

The sum of two (not necessarily distinct) abundant numbers, i.e., A048260.

See also a005101.

\(a(n) = \sum_{k=1}^n \phi(2k)\), i.e., A049690.

See also a000010 and a002088.

Smallest number whose sum of digits is \(n\), i.e. A051885.

See also a007953 and digitSum.

Number of divisors of \(n\) that are smaller than \(\sqrt{n}\), i.e. A056924.

\(a056924(n) = N(4n)\) from Project Euler Problem 174: Hollow Square Laminae II.

Number of nonsquarefree numbers not exceeding \(n\), i.e., A057627.

\(a060735(1) = 1\), \(a060735(2) = 2\); thereafter, \(a060735(n)\) is the smallest number \(m\) not yet in the sequence such that every prime that divides \(a(n-1)\) also divides \(m\), i.e. A060735.

See a007947.

Numbers of the form \(x(x+1)y(y+1)\) ("bipronics") with \(x\) and \(y\) nonnegative integers, i.e., A072389.

See a002378.

\(a076314(n) = \lfloor \frac{n}{10} \rfloor + (n \bmod 10)\), i.e. A0076314.

Numbers of the form \(p^{q}q^{p}\), with distinct primes \(p\) and \(q\), i.e., A082949.

Numbers \(k\) such that \(3k^2 + 3k + 1\) is prime, i.e. A111251.

\(\binom{n}{2}\), i.e., A161680.

The number of base-10 bouncy numbers below \(10^{n}\), i.e., A204692.

Number of integer pairs \((x,y,)\) such that \(0 < x < y \leq n\) and \(xy \leq n\), i.e., A211264.

See a007953.

The distinct prime factors of a given number.

>>> distinctPrimeFactors 504
2 :| [3,7]

See also a007947 and a027748.

See a000384.

Determine whether a given number is pentagonal, i.e., a member of a000326.

See a000326.

See a000330.

See a000290.

See a000217.