Sequences

Primorial numbers (first definition): product of first n primes. Sometimes written prime(n)#.

Glaisher's G numbers.

Glaisher's H numbers.

Palindromes in base 10.

Glaisher's H' numbers.

Generalized Euler numbers.

Some special numbers.

Apéry's number or Apéry's constant zeta(3). Decimal expansion of zeta(3) = Sum_{m >= 1} 1/m^3.

5th powers written backwards.

Bessel polynomial y_n(-2).

a(1) = 0, a(2) = -2; for n > 2, a(n) + a(n-2) - a(n-3) - a(n-5) - ... - a(n-p) = (-1)^(n+1)*n if n is prime, otherwise = 0, where p = largest prime < n.

a(0) = 1, a(1) = 0, a(2) = -1; for n >= 3, a(n) = - a(n-2) + Sum_{ primes p with 3 <= p <= n} a(n-p).

a(n) = Sum_{t=0..n} g(t)*g(n-t) where g(t) = A002121(t).

a(1) = 0, a(2) = 0; for n > 2, a(n) - a(n-3) - a(n-5) - ... - a(n-p) = n if n is prime, otherwise = 0, where p = largest prime < n.

Number of compositions of n into a sum of odd primes.

a(n) = Sum_{k=0..n} f(k)*f(n-k) where f(k) = A002124(k).

Number of solutions to n=p+q where p and q are primes or zero.

MacMahon's generalized sum of divisors function.

MacMahon's generalized sum of divisors function.

Generalized sum of divisors function: excess of sum of odd divisors of n over sum of even divisors of n.

Generalized sum of divisors function.

Sum of divisors d of n such that n/d is odd.

Generalized sum of divisors function.

Number of partitions of n with exactly two part sizes.

Generalized divisor function. Number of partitions of n with exactly three part sizes.

Number of terms in a symmetrical determinant: a(n) = n*a(n-1) - (n-1)*(n-2)*a(n-3)/2.

Matrices with 2 rows.

Number of n X n symmetric matrices with nonnegative integer entries, trace 0 and all row sums 2.

6th powers written backwards.

Shuffling 2n cards.

7th powers written backwards.

Class numbers of quadratic fields.

Primes p == 1 (mod 4) where class number of Q(sqrt p) increases.

Class numbers h(-p) where p runs through the primes p == 3 (mod 4).

Pythagorean primes: primes of the form 4*k + 1.

Primes of the form 4*k + 3.

Smallest prime == 7 (mod 8) where Q(sqrt(-p)) has class number 2n+1.

Largest prime == 7 (mod 8) with class number 2n+1.

Smallest prime p==3 (mod 8) such that Q(sqrt(-p)) has class number 2n+1.

Largest prime p==3 (mod 8) such that Q(sqrt(-p)) has class number 2n+1.

Numbers k for which the rank of the elliptic curve y^2 = x^3 - k is 0.

Numbers k for which rank of the elliptic curve y^2 = x^3 + k is 0.

Numbers k for which the rank of the elliptic curve y^2 = x^3 - k is 1.

Numbers k for which the rank of the elliptic curve y^2 = x^3 + k is 1.

Numbers k for which the rank of the elliptic curve y^2 = x^3 - k is 2.

Numbers k for which the rank of the elliptic curve y^2 = x^3 + k is 2.

Numbers k for which the rank of the elliptic curve y^2 = x^3 - k*x is 0.

Numbers k for which the rank of the elliptic curve y^2 = x^3 - k*x is 1.

Numbers k for which the rank of the elliptic curve y^2 = x^3 + k*x is 0.

Numbers k for which the rank of the elliptic curve y^2 = x^3 + k*x is 1.