OFFSET
2,2
REFERENCES
Vladimir S. Shevelev, Multiplicative functions in the Fermi-Dirac arithmetic, Izvestia Vuzov of the North-Caucasus region, Nature sciences 4 (1996), 28-43 [Russian].
LINKS
Chai Wah Wu, Table of n, a(n) for n = 2..10000 (terms 2..1000 from Amiram Eldar)
Simon Litsyn and Vladimir Shevelev, On factorization of integers with restrictions on the exponent, INTEGERS: Electronic Journal of Combinatorial Number Theory, 7 (2007), #A33, 1-36.
FORMULA
a(n) = Sum_{i} A000120(e_i), where n! = Product_{i} p_i^e_i is the prime factorization of n!.
a(n) = A064547(n!). - R. J. Mathar, May 28 2010
MAPLE
read("transforms") ; A064547 := proc(n) f := ifactors(n)[2] ; a := 0 ; for p in f do a := a+wt(op(2, p)) ; end do: a ; end proc:
MATHEMATICA
f[p_, e_] := DigitCount[e, 2, 1]; a[1] = 0; a[n_] := Plus @@ f @@@ FactorInteger[n!]; Array[a, 100, 2] (* Amiram Eldar, Aug 24 2024 *)
PROG
(Python)
from collections import Counter
from sympy import factorint
def A177329(n): return sum(map(int.bit_count, sum((Counter(factorint(i)) for i in range(2, n+1)), start=Counter()).values())) # Chai Wah Wu, Jul 18 2024
(PARI) a(n) = vecsum(apply(x -> hammingweight(x), factor(n!)[, 2])); \\ Amiram Eldar, Aug 24 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, May 06 2010
EXTENSIONS
I inserted one omitted term: a(20)=10. Vladimir Shevelev, May 08 2010
Terms from a(14) onwards replaced according to the formula - R. J. Mathar, May 28 2010
STATUS
approved