A113903 Sum of omega(n!) and bigomega(n!).

0, 0, 2, 4, 6, 8, 10, 12, 15, 17, 19, 21, 24, 26, 28, 30, 34, 36, 39, 41, 44, 46, 48, 50, 54, 56, 58, 61, 64, 66, 69, 71, 76, 78, 80, 82, 86, 88, 90, 92, 96, 98, 101, 103, 106, 109, 111, 113, 118, 120, 123, 125, 128, 130, 134, 136, 140, 142, 144, 146, 150, 152, 154, 157

Offset

0,3

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Formula

a(n) = A000720(n) + A022559(n). - Michel Marcus, Nov 22 2024

Maple

p:= 0: w:= 0: R:= 0:
for n from 1 to 100 do
  if isprime(n) then p:= p+1 fi;
  w:= w+numtheory:-bigomega(n);
  R:= R, p+w
od:
R; # Robert Israel, Nov 21 2024

Mathematica

Join[{0}, Accumulate[Array[Boole[PrimeQ[#]] + PrimeOmega[#] &, 100]]] (* Paolo Xausa, Nov 22 2024 *)

Prog

(PARI) a(n) = omega(n!) + bigomega(n!);

Crossrefs

Cf. A000142, A001221, A001222.

Cf. A000720, A022559.

Partial sums of A378309 (for n >= 1).

Sequence in context: A287122 A064997 A292651 * A248563 A278453 A347009

Adjacent sequences: A113900 A113901 A113902 * A113904 A113905 A113906

Keyword

easy,nonn

Author

Cino Hilliard, Jan 29 2006

Status

approved