A163106 a(n) = sigma(sigma(tau(n))), where tau = number of divisors and sigma = sum of divisors.

1, 4, 4, 7, 4, 8, 4, 8, 7, 8, 4, 28, 4, 8, 8, 12, 4, 28, 4, 28, 8, 8, 4, 24, 7, 8, 8, 28, 4, 24, 4, 28, 8, 8, 8, 14, 4, 8, 8, 24, 4, 24, 4, 28, 28, 8, 4, 39, 7, 28, 8, 28, 4, 24, 8, 24, 8, 8, 4, 56, 4, 8, 28, 15, 8, 24, 4, 28, 8, 24, 4, 56, 4, 8, 28, 28, 8, 24, 4, 39, 12, 8, 4, 56, 8, 8, 8, 24, 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..10000

Crossrefs

Cf. A000005, A000203, A051027, A062069.

Programs

Maple

with(numtheory) : A163106 := proc(n) sigma(sigma(tau(n))) ; end: seq(A163106(n),n=1..120) ; # R. J. Mathar, Jul 27 2009

Mathematica

DivisorSigma[1,DivisorSigma[1,DivisorSigma[0,Range[90]]]] (* Harvey P. Dale, Oct 14 2017 *)

PARI

A163106(n) = sigma(sigma(numdiv(n))); \\ Antti Karttunen, May 25 2017

Formula

a(n) = A000203(A000203(A000005(n))) = A000203(A062069(n)) = A051027(A000005(n)).

Extensions

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