A066088 Number of distinct prime factors of sigma_2(n), where sigma_2(n) = A001157(n).

0, 1, 2, 2, 2, 2, 2, 2, 2, 3, 2, 4, 3, 2, 3, 2, 3, 3, 2, 4, 2, 3, 3, 3, 3, 3, 3, 4, 2, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 4, 2, 2, 3, 4, 3, 3, 4, 4, 3, 4, 3, 5, 3, 3, 3, 3, 3, 3, 2, 5, 2, 4, 4, 2, 4, 3, 3, 5, 3, 3, 2, 4, 4, 3, 5, 4, 3, 3, 2, 4, 2, 3, 4, 4, 4, 3, 3, 4, 3, 4, 3, 5, 4, 4, 3, 5, 3, 4, 4, 3, 2, 3, 3, 3, 3

Offset: 1

Author

Labos Elemer, Dec 04 2001

Keywords

• nonn

Examples

			sigma_2(12) = 144 + 36 + 16 + 9 + 4 + 1 = 210, so a(12)=4.
		

Links

• Harry J. Smith, Table of n, a(n) for n=1..1000

Crossrefs

Cf. A001157, A001221.

Programs

Mathematica

PrimeNu[DivisorSigma[2,Range[110]]] (* Harvey P. Dale, Feb 23 2015 *)

PARI

a(n) = { omega(sigma(n, 2)) } \\ Harry J. Smith, Nov 11 2009

Formula

a(n) = A001221(A001157(n)).

Extensions

Offset changed from 0 to 1 by Harry J. Smith, Nov 11 2009