A058062 Number of distinct prime factors of sigma(n), the sum of the divisors of n.

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

Offset: 1

Author

Labos Elemer, Nov 23 2000

Keywords

• nonn

Examples

			n=81, sigma(81) = 81+27+9+3+1 = 121 = 11^2, so a(81) = 1.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5001

Crossrefs

Cf. A001221, A000203.

Programs

Mathematica

Table[PrimeNu[DivisorSigma[1, n]], {n, 50}] (* G. C. Greubel, May 20 2017 *)

PARI

for(n=1,50, print1(omega(sigma(n)), ", ")) \\ G. C. Greubel, May 20 2017

Formula

a(n) = A001221(A000203(n)).

Extensions

Offset corrected by Sean A. Irvine, Jul 22 2022