A243129 a(n) = sigma(d(d(d(n)))), where d(n) is the number of divisors of n.

1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 3, 4, 4, 3, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 3, 3, 7, 3, 3, 4, 3, 3, 4, 3, 4, 3, 4, 3, 7, 3, 3, 4, 4, 3, 4, 3, 4, 3, 3, 3, 7, 3, 3

Offset

1,2

Comments

a(n) >= 3 for n > 1 with a(1) = 1. If n is a prime or a semiprime, a(n) = 3. The converse is not true since a(8) = 3, but 8 is neither a prime nor a semiprime.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

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

Example

a(12) = 4; 12 has 6 divisors --> 6 has 4 divisors --> 4 has 3 divisors --> and the sum of the divisors of 3 is 4.

Maple

with(numtheory); A243129:=n->sigma(tau(tau(tau(n)))); seq(A243129(n), n=1..100);

Mathematica

Table[DivisorSigma[1, DivisorSigma[0, DivisorSigma[0, DivisorSigma[0, n]]]], {n, 100}]
Table[DivisorSigma[1, Nest[DivisorSigma[0, #]&, n, 3]], {n, 100}] (* Harvey P. Dale, Mar 24 2016 *)

Crossrefs

Cf. A000005, A000203.

Sequence in context: A175797 A358475 A335550 * A135717 A335465 A079083

Adjacent sequences: A243126 A243127 A243128 * A243130 A243131 A243132

Keyword

nonn,easy

Author

Wesley Ivan Hurt, May 29 2014

Status

approved