A113902 Product of omega(n!) and bigomega(n!).

0, 1, 4, 8, 15, 21, 32, 44, 52, 60, 80, 95, 120, 132, 144, 168, 203, 224, 264, 288, 304, 320, 369, 405, 423, 441, 468, 495, 560, 590, 660, 715, 737, 759, 781, 825, 912, 936, 960, 1008, 1105, 1144, 1246, 1288, 1330, 1358, 1470, 1545, 1575, 1620, 1650, 1695

Offset

1,3

Comments

omega(x!) is the number of primes <= x.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

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

a(n) = A000720(n)*A022559(n). - Michael De Vlieger, Nov 22 2024

Maple

p:= 0: w:= 0: R:= 0:
for n from 2 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

PrimeNu[#]PrimeOmega[#]&/@(Range[60]!) (* Harvey P. Dale, Aug 14 2013 *)

Prog

(PARI) omegafactxbigomegafact(n) = { local(x); for(x=1, n, print1(omega(x!)*bigomega(x!)", ") ) }

Crossrefs

Cf. A000142, A000720, A001221, A001222, A022559.

Sequence in context: A071422 A368897 A212538 * A024916 A212539 A102216

Adjacent sequences: A113899 A113900 A113901 * A113903 A113904 A113905

Keyword

easy,nonn,changed

Author

Cino Hilliard, Jan 29 2006

Status

approved