A058063 Number of prime factors (when counted with multiplicity) of sigma(n), the sum of divisors of n.

0, 1, 2, 1, 2, 3, 3, 2, 1, 3, 3, 3, 2, 4, 4, 1, 3, 2, 3, 3, 5, 4, 4, 4, 1, 3, 4, 4, 3, 5, 5, 3, 5, 4, 5, 2, 2, 4, 4, 4, 3, 6, 3, 4, 3, 5, 5, 3, 2, 2, 5, 3, 4, 5, 5, 5, 5, 4, 4, 5, 2, 6, 4, 1, 4, 6, 3, 4, 6, 6, 5, 3, 2, 3, 3, 4, 6, 5, 5, 3, 2, 4, 4, 6, 5, 4, 5, 5, 4, 4, 5, 5, 7, 6, 5, 5, 3, 3, 4, 2, 3, 6, 4, 4, 7

Offset: 1

Author

Labos Elemer, Nov 23 2000

Keywords

• nonn

Examples

			n=35, sigma(35) = 35 + 5 + 7 + 1 = 48 = 2*2*2*2*3, so a(35)=5.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences related to sums of divisors

Crossrefs

Cf. A000120, A000203, A001222, A331750, A332221.

Programs

Maple

with(numtheory):a:=proc(n) if n=0 then 0 else bigomega(sigma(n)) fi end: seq(a(n), n=1..105); # Zerinvary Lajos, Apr 11 2008

Mathematica

Array[PrimeOmega@ DivisorSigma[1, #] &, 105] (* Michael De Vlieger, Nov 08 2017 *)

PARI

a(n) = bigomega(sigma(n)); \\ Michel Marcus, Nov 07 2017

Formula

a(n) = A001222(A000203(n)).

From Antti Karttunen, Feb 12 2020: (Start)

Additive with a(p^e) = A001222(A000203(p^e)) = A001222(1 + p + p^2 + ... + p^e).

a(n) = A000120(A332221(n)).

(End)

Extensions

Offset corrected by Antti Karttunen, Nov 07 2017