A342658 Number of prime factors in the n-th multiply perfect number, counted with multiplicity: a(n) = bigomega(A007691(n)).

0, 2, 3, 5, 5, 7, 7, 10, 8, 12, 9, 15, 13, 14, 15, 13, 14, 17, 17, 17, 18, 18, 19, 20, 19, 20, 20, 21, 16, 21, 22, 18, 24, 26, 22, 19, 24, 29, 19, 22, 31, 29, 21, 32, 31, 26, 28, 28, 33, 35, 34, 34, 37, 37, 35, 34, 35, 35, 36, 33, 38, 38, 37, 39, 42, 42, 39, 46, 40, 42, 48, 39, 38, 46, 40, 40, 47, 41, 44, 46, 43, 39

Offset: 1

Author

Antti Karttunen, Mar 19 2021

Keywords

• nonn
• look

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1600

Crossrefs

Cf. A001222, A007691.

Cf. also A134740, A342659, A342660.

Programs

Mathematica

Select[Range[10^6], IntegerQ@ DivisorSigma[-1, #] &] (* or, using the b-file at A007691: *)
Map[PrimeOmega, DeleteCases[Import["https://oeis.org/A007691/b007691.txt", "Data"], ?(Length@ # == 0 &)][[1 ;; 82, -1]] ] (* _Michael De Vlieger, Mar 19 2021 *)

Formula

a(n) = A001222(A007691(n)).

a(n) >= A134740(n).