A163105 a(n) = tau(sigma(tau(n))), where tau = number of divisors of n (A000005), and sigma = sum of divisors of n (A000203).

1, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 6, 2, 2, 2, 4, 2, 6, 2, 6, 2, 2, 2, 4, 3, 2, 2, 6, 2, 4, 2, 6, 2, 2, 2, 2, 2, 2, 2, 4, 2, 4, 2, 6, 6, 2, 2, 6, 3, 6, 2, 6, 2, 4, 2, 4, 2, 2, 2, 6, 2, 2, 6, 4, 2, 4, 2, 6, 2, 4, 2, 6, 2, 2, 6, 6, 2, 4, 2, 6, 4, 2, 2, 6, 2, 2, 2, 4, 2, 6, 2, 6, 2, 2, 2, 6, 2, 6, 6, 2, 2, 4, 2, 4, 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..10000

Index entries for sequences computed from exponents in factorization of n

Formula

a(n) = A000005(A000203(A000005(n))) = A000005(A062069(n)) = A062068(A000005((n)).

Maple

with(numtheory) : A163105 := proc(n) tau(sigma(tau(n))) ; end: seq(A163105(n), n=1..120) ; # R. J. Mathar, Jul 27 2009

Prog

(PARI) A163105(n) = numdiv(sigma(numdiv(n))); \\ Antti Karttunen, Jul 23 2017

Crossrefs

Cf. A000005, A000203, A062068, A062069, A163106.

Sequence in context: A134852 A071188 A078545 * A152235 A278966 A123582

Adjacent sequences: A163102 A163103 A163104 * A163106 A163107 A163108

Keyword

nonn

Author

Jaroslav Krizek, Jul 20 2009

Extensions

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

Name edited by Antti Karttunen, Jul 23 2017

Status

approved