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

1,2

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

Formula

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

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 *)

Prog

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

Crossrefs

Cf. A000005, A000203, A010553, A062068.

Sequence in context: A151714 A039644 A281945 * A275840 A178065 A366636

Adjacent sequences: A163104 A163105 A163106 * A163108 A163109 A163110

Keyword

nonn

Author

Jaroslav Krizek, Jul 20 2009

Extensions

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

Status

approved