Sequences

Duplicate of A006055.

Largest inverse of totient function (A000010): a(n) is the largest x such that phi(x) = m, where m = A002202(n) is the n-th number in the range of phi.

Greater of twin primes.

Limit of the image of n after 2k iterates of `(3x+1)/2' map as k grows.

Primes p such that 2^p - 1 has at most 2 prime factors.

Mersenne numbers with at most 2 prime factors.

a(n) = 2^(n-1)*(2^n - 1), n >= 0.

Numbers k such that k divides 2^k + 2.

Continued fraction for Sum_{k >= 2} 2^(-Fibonacci(k)).

Highest power of 2 dividing n.

Partial sums of A006519.

Numbers n such that n divides 2^n + 1.

4-dimensional analog of centered polygonal numbers. Also number of regions created by sides and diagonals of a convex n-gon in general position.

Sum ((-1)^(i+1)*binomial(n,i)*2^i*(2*n-1)!,i=1..n) for n odd.

Egyptian fraction for 1/ Pi.

Denominators of greedy Egyptian fraction for e - 2.

Egyptian fraction for 1/e.

a(n) = (n^3 + 2*n)/3.

a(n) = (n^4 + n^2 + 2*n)/4.

a(n) = (25*n^4-120*n^3+209*n^2-108*n)/6.

Gpf(n): greatest prime dividing n, for n >= 2; a(1)=1.

Semiorders on n elements.

Numbers whose sum of divisors is a square.

Place n equally-spaced points around a circle and join every pair of points by a chord; this divides the circle into a(n) regions.

Number of one-sided triangular polyominoes (n-iamonds) with n cells; turning over not allowed, holes are allowed.

Number of one-sided hexagonal polyominoes with n cells.

Switching classes of digraphs.

Worst cases for Pierce expansions (numerators).

Worst cases for Pierce expansions (denominators).

Numerators of worst case for Engel expansion.

Denominators of worst case for Engel expansion.

Number of dissimilarity relations on an n-set.

a(n) = binomial(n,3)*binomial(n-1,3)/4.

Maximal iterated binomial coefficients.

Number of stable forests with n nodes.

Number of stable unicyclic graphs with n nodes.

Number of elements (a b, c d) in SL(2,Z) with trace n and 0 <= a <= {b, c} <= d.

Sum ((-1)^(i+1)*binomial(n,i)*2^i*(2*i-1)!,i=1..n).

(2*n)!-Sum ((-1)^(i+1)*binomial(n,i)*2^i*(2*n-1)!,i=1..n).

Numbers k such that k and k+1 are prime powers.

n+8*C(n,2)+30*C(n,3)+62*C(n,4)+75*C(n,5)+30*C(n,6).

Maximal Eulerian numbers.

Numbers k such that k*3^k + 1 is prime.

Numbers k such that k*3^k - 1 is prime.

Minimal discriminant of totally real number field of degree n.

Minimal absolute value of discriminants of number fields of degree n with exactly 2 (1 pair of) complex embeddings.

Number of different cycles of digits in the decimal expansions of 1/p, 2/p, ..., (p-1)/p where p = n-th prime different from 2 or 5.

Minimal absolute value of discriminants of number fields of degree n.

Start of first run of n consecutive integers with same number of divisors.

Short period primes: the decimal expansion of 1/p has period less than p-1, but greater than zero.