login
A375635
The number of infinitary divisors of n!.
4
1, 1, 2, 4, 8, 16, 8, 16, 64, 64, 16, 32, 128, 256, 512, 1024, 2048, 4096, 256, 512, 512, 2048, 4096, 8192, 8192, 16384, 32768, 65536, 16384, 32768, 65536, 131072, 524288, 2097152, 131072, 65536, 32768, 65536, 131072, 262144, 524288, 1048576, 4194304, 8388608
OFFSET
0,3
LINKS
FORMULA
a(n) = A037445(n!).
a(n) = 2^A177329(n).
A048656(n) <= a(n) <= A027423(n).
MATHEMATICA
f[p_, e_] := 2^DigitCount[e, 2, 1]; a[0] = a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n!]; Array[a, 100, 0]
PROG
(PARI) a(n) = vecprod(apply(x -> 2^hammingweight(x), factor(n!)[, 2]));
(Python)
from collections import Counter
from sympy import factorint
def A375635(n): return 1<<sum(e.bit_count() for e in sum((Counter(factorint(i)) for i in range(2, n+1)), start=Counter()).values()) # Chai Wah Wu, Aug 22 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Aug 22 2024
STATUS
approved