A055636 Partial sums of A144494.

0, 0, 0, 2, 2, 4, 4, 7, 9, 11, 11, 14, 14, 16, 18, 22, 22, 25, 25, 28, 30, 32, 32, 36, 38, 40, 43, 46, 46, 49, 49, 54, 56, 58, 60, 64, 64, 66, 68, 72, 72, 75, 75, 78, 81, 83, 83, 88, 90, 93, 95, 98, 98, 102, 104, 108, 110, 112, 112, 116, 116, 118, 121, 127, 129, 132, 132

Offset: 1

Author

Labos Elemer, Jun 07 2000

Keywords

• nonn

Comments

Excess of prime-power exponents in n!.

Examples

			n=46: prime powers in factorization of 46! are {42,21,10,6,4,3,2,2,2,1,1,1,1,1}. Sum of the exponents is 97. It has 14 distinct prime divisors, so a(46)=97-14=83.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A046660, A000142, A022559, A001221, A001222, A000720, A144494.

Programs

Mathematica

Table[PrimeOmega[n!] - PrimeNu[n!], {n, 1, 100}] (* G. C. Greubel, May 13 2017 *)

PARI

for(n=1,100, print1(bigomega(n!) - omega(n!), ", ")) \\ G. C. Greubel, May 13 2017

Formula

a(n) = A046660(n!) = A046660(A000142(n)) = A022559(n) - A001221(n!) = A001222(n!) - A000720(n).

Extensions

Simpler definition from Alan Worley (aw(AT)xiboo.co.uk), Dec 10 2008