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

Comments

omega(x!) = number of primes <= x or Pi(x)

Links

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

Formula

omega(x): number of distinct prime divisors of x. bigomega(x): number of prime divisors of x, counted with multiplicity.

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

Prog

(PARI) omegafactpbigomegafact(n) = { local(x); for(x=0, n, print1(omega(x!)+bigomega(x!)", ") ) }

Crossrefs

Sequence in context: A287122 A064997 A292651 * A248563 A278453 A347009

Adjacent sequences: A113900 A113901 A113902 * A113904 A113905 A113906

Keyword

easy,nonn,changed

Author

Cino Hilliard, Jan 29 2006

Status

approved