A163107 a(n) = tau(tau(sigma(n))), where tau = A000005, the number of divisors, and sigma = A000203, the sum of divisors of n.

1, 2, 2, 2, 3, 4, 3, 3, 2, 4, 4, 4, 3, 4, 4, 2, 4, 3, 4, 4, 4, 3, 4, 6, 2, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4, 3, 3, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 4, 3, 3, 6, 4, 4, 5, 6, 5, 4, 6, 6, 5, 3, 6, 4, 2, 6, 4, 4, 6, 6, 4, 6, 4, 3, 4, 4, 6, 6, 5, 4, 4, 2, 6, 6, 6, 6, 6, 5, 6, 6, 6, 4, 5, 4, 4, 5, 6, 4, 4, 6, 3, 4, 5, 4, 5, 4

Offset: 1

Author

Jaroslav Krizek, Jul 20 2009

Keywords

• nonn

Comments

Repeated application of tau (number of divisors) and sigma (sum of divisors).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A000005, A000203, A010553, A062068.

Programs

Maple

with(numtheory) : A163107 := proc(n) tau(tau(sigma(n))) ; end: seq(A163107(n),n=1..120) ; # R. J. Mathar, Jul 27 2009

Mathematica

DivisorSigma[0,DivisorSigma[0,DivisorSigma[1,Range[110]]]] (* Harvey P. Dale, Nov 25 2016 *)

PARI

A163107(n) = numdiv(numdiv(sigma(n))); \\ Antti Karttunen, Nov 07 2017

Formula

a(n) = A000005(A000005(A000203(n))) = A000005(A062068(n)) = A010553(A000203(n)).

Extensions

More terms from R. J. Mathar, Jul 27 2009