Sequences

Primes that contain digits 3 and 4 only.

Primes that contain digits 3 and 5 only.

Primes that contain digits 3 and 7 only.

Primes that contain digits 3 and 8 only.

Primes that contain digits 4 and 7 only.

Primes that contain digits 4 and 9 only.

Primes that contain digits 5 and 7 only.

Primes that contain digits 5 and 9 only.

Primes that contain digits 6 and 7 only.

Primes that contain digits 7 and 8 only.

Primes that contain digits 7 and 9 only.

Primes that contain digits 8 and 9 only.

Egyptian fractions: number of partitions of 1 into reciprocals of positive integers <= n.

A Motzkin triangle: a(n,k), n >= 2, 2 <= k <= n, = number of complete, strictly subdiagonal staircase functions.

a(n) is the number of k for which binomial(n,k) is divisible by n.

Numbers k such that the sum of divisors of k^3 is a cube.

Numbers whose sum of divisors is a cube.

Number of singular 2 X 2 matrices over Z(n) (i.e., with determinant = 0).

Number of noninvertible 2 X 2 matrices over Z/nZ (determinant is a divisor of 0).

Primes p which divide no f(q)-1 or f(q)+1 for prime q < p, where f(q) is the product of all primes <= q.

Least p with p, q both prime, p+q = 2n.

Greatest p with p, q both prime, p+q = 2n.

Least prime p such that p+2n is also prime.

Least prime p such that there exists a prime q with p-2n = q.

Least positive palindromic multiple of n, or 0 if none exists.

Average of squares of divisors is an integer: numbers k such that sigma_0(k) divides sigma_2(k).

Antiharmonic numbers: numbers k such that sigma_1(k) divides sigma_2(k).

Numbers n such that tau(n) (or sigma_0(n)) = phi(n).

Numbers k such that phi(k) divides sigma_0(k).

Numbers k such that phi(k) <= sigma_0(k).

Numbers k such that sigma_0(k) divides phi(k).

Balanced numbers: numbers k such that phi(k) (A000010) divides sigma(k) (A000203).

Numbers k such that d(k) (number of divisors) divides phi(k) (Euler function) divides sigma(k) (sum of divisors).

Expansion of 1/((1-5x)(1-9x)(1-10x)).

Neither square nor square + prime.

From the ground state energy of a variant of the Hubbard Hamiltonian for 2 holes on a lattice of n sites.

Conjecturally, this is the minimal y such that n primes occur infinitely often among (x+1, ..., x+y), that is, pi(x+y) - pi(x) >= n for infinitely many x.

a(n) is the least number > a(n-1) such that there is no prime p for which a(1) through a(n) would contain all residues modulo p.

Expansion of 1/((1-5x)(1-9x)(1-11x)).

Cyclotomic polynomials at x=1.

Cyclotomic polynomials at x=-2.

Cyclotomic polynomials at x=-3.

Cyclotomic polynomials at x=-4.

Cyclotomic polynomials at x=-5.

Cyclotomic polynomials at x=-6.

Cyclotomic polynomials at x = -7.

Cyclotomic polynomials at x=-8.

Cyclotomic polynomials at x=-9.

Cyclotomic polynomials at x=-10.

Cyclotomic polynomials at x=-11.