Sequences

9-gonal square numbers.

Number of empty intervals when fractional_part(i*e) for i = 1, ..., n is plotted along [ 0, 1 ] subdivided into n equal regions.

Values of k for which there are no empty intervals when fractional_part(m*e) for m = 1, ..., k is plotted along [ 0, 1 ] subdivided into k equal regions.

Number of empty intervals when fractional_part(i*phi) for i = 1, ..., n is plotted along [ 0, 1 ] subdivided into n equal regions.

Values of k for which there are no empty intervals when fractional part(m*phi) for m = 1, ..., k is plotted along [ 0, 1 ] subdivided into k equal regions.

Number of empty intervals when fractional_part(i*Pi) for i = 1, ..., n is plotted along [ 0, 1 ] subdivided into n equal regions.

Values of k for which there are no empty intervals when fractional part(m*Pi) for m = 1, ..., k is plotted along [ 0, 1 ] subdivided into k equal regions.

Number of self-avoiding polygons with perimeter n on hexagonal [ =triangular ] lattice.

Number of ternary rooted trees with n nodes and height exactly 4.

Number of ternary rooted trees with n nodes and height exactly 5.

Number of ternary rooted trees with n nodes and height exactly 6.

Number of ternary rooted trees with n nodes and height exactly 7.

Number of ternary rooted trees with n nodes and height exactly 8.

Number of ternary rooted trees with n nodes and height exactly 9.

Number of ternary rooted trees with n nodes and height exactly 10.

Number of ternary rooted trees with n nodes and height exactly 11.

Number of ternary rooted trees with n nodes and height exactly 12.

Square octagonal numbers.

Primes related to Carmichael numbers of the form pqr, p<q<r and p-1 a divisor of both q-1 and r-1.

Number of iterations needed to reach 1 under the map n -> Omega(n).

a(n) = number of positive integers b which, when added to the number of their divisors, tau(b), gives n.

Sets a record for the number of positive integers which, when added to the number of their divisors, gives n.

Number of divisors is a digit in the base 10 representation of n.

Integers which cannot be written as k+tau(k) for some k.

Digits are nonzero squares.

Numbers whose number of divisors is a square.

Triangle of coefficients of generating function of ternary rooted trees of height exactly n.

Integers which can be written as m*tau(m) for some m, where tau = A000005.

a(n) = a(n-1) + prime(n-1), with a(1)=2.

Number of ways of arranging row n of the prime pyramid.

a(n+1) = next number having largest prime dividing a(n) as a factor, with a(1) = 2.

a(n) = 2^((n-1)*(n+2)/2).

Number of ternary rooted trees with n nodes and height exactly 3.

Integer-sided squares, no more than a(n) of any size, can tile the square with side n.

Maximum size of smallest square when a square of side n is tiled with integer-sided squares.

Not of form sigma(k) - phi(k).

Double and reverse digits.

Smallest positive number containing n e's when spelled out in US English.

Values square, differences triangular.

a(n) = d(d(d(n))), the 3rd iterate of the number-of-divisors function with an initial value of n.

Maximal value of d(x) (the number of divisors of x, A000005) if the binary order (see A029837) of x, the value g(x) = n.

a(n) = d(d(d(d(n)))), the 4th iterate of number-of-divisors function with initial value of n.

a(n) = d(d(d(d(d(n))))), the 5th iterate of the number-of-divisors function d = A000005, with initial value n.

Prime powers with special exponents: q^(p-1) where p > 2 and q are prime numbers.

Numbers n such that d(d(n)) is an odd prime, where d(k) is the number of divisors of k.

Numbers k for which exactly 4 applications of A000005 are needed to reach 2.

Numbers k for which exactly 5 applications of A000005 are needed to reach 2.

For all n, if d is recursively applied to a(n) exactly 6 times then the fixed point of d-iteration is just reached.

Number of iterations required to reach stationary value when repeatedly applying d, the number of divisors function (A000005).

Erroneous version of A009287 (the 2 should be omitted).