A264440 Row lengths of the irregular triangle A137510 (number of divisors d of n with 1 < d < n, or 0 if no such d exists).

1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 2, 3, 1, 4, 1, 4, 2, 2, 1, 6, 1, 2, 2, 4, 1, 6, 1, 4, 2, 2, 2, 7, 1, 2, 2, 6, 1, 6, 1, 4, 4, 2, 1, 8, 1, 4, 2, 4, 1, 6, 2, 6, 2, 2, 1, 10, 1, 2, 4, 5, 2, 6, 1, 4, 2, 6, 1, 10, 1, 2, 4, 4, 2, 6, 1, 8, 3, 2, 1, 10, 2, 2

Offset: 1

Author

Wolfdieter Lang, Jan 16 2016

Keywords

• nonn
• easy

Comments

See A032741 for the number of divisors d of n with 1 <= d < n, n >= 1.

See A070824 for the number of the divisors d of n with 1 < d < n, n >= 1.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A000040, A032741, A070824, A137510.

Programs

Maple

seq(max(1,numtheory:-tau(n)-2), n=1..100); # Robert Israel, Jan 20 2016

Mathematica

Array[DivisorSigma[0, #] - 2 &, {80}] /. n_ /; n < 2 -> 1 (* Michael De Vlieger, Jan 16 2016 *)

PARI

A264440(n) = max(1,numdiv(n)-2); \\ After Robert Israel's formula. - Antti Karttunen, May 25 2017

Formula

a(1) = 1; a(n) = 1 if n is prime, otherwise a(n) = A070824(n).

a(1) = 1; a(n) = 1 if n is prime, otherwise a(n) = A032741(n) - 1.

a(n) = max(1, A000005(n)-2). - Robert Israel, Jan 20 2016