A066088 Number of distinct prime factors of sigma_2(n) = A001157(n), the sum of squares of divisors of 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

1,3

Links

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

Formula

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

Example

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

Mathematica

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

Prog

(PARI) { for (n=1, 1000, a=omega(sigma(n, 2)); write("b066088.txt", n, " ", a) ) } \\ Harry J. Smith, Nov 11 2009

Crossrefs

Cf. A001157, A001221.

Sequence in context: A278950 A029411 A165093 * A139326 A029243 A306240

Adjacent sequences: A066085 A066086 A066087 * A066089 A066090 A066091

Keyword

nonn

Author

Labos Elemer, Dec 04 2001

Extensions

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

Status

approved