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

1,4

Comments

Excess of prime-power exponents in n!.

Links

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

Formula

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A056503 A256217 A361439 * A206559 A143419 A183566

Adjacent sequences: A055633 A055634 A055635 * A055637 A055638 A055639

Keyword

nonn

Author

Labos Elemer, Jun 07 2000

Extensions

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

Status

approved