A375850 The maximum even exponent in the prime factorization of n!, or 0 if no such exponent exists.

0, 0, 0, 0, 0, 0, 4, 4, 2, 4, 8, 8, 10, 10, 2, 6, 6, 6, 16, 16, 18, 18, 4, 4, 22, 22, 10, 6, 6, 6, 26, 26, 14, 4, 32, 32, 34, 34, 8, 18, 38, 38, 6, 6, 6, 10, 42, 42, 46, 46, 22, 12, 12, 12, 50, 50, 26, 4, 54, 54, 56, 56, 28, 30, 30, 30, 64, 64, 66, 66, 32, 32, 70

Offset

0,7

Comments

The sequence of indices of record values, 0, 6, 10, 12, 18, 20, 24, 30, 34, 36, 40, ..., are the evil numbers (A001969) multiplied by 2 (A125592).

Links

Amiram Eldar, Table of n, a(n) for n = 0..10000

Index entries for sequences related to factorial numbers.

Formula

a(n) = A375033(n!).

max(a(n), A375849(n)) = A011371(n).

Mathematica

a[n_] := Max[0, Max[Select[FactorInteger[n!][[;; , 2]], EvenQ]]]; Array[a, 100, 0]

Prog

(PARI) a(n) = {my(e = select(x -> !(x % 2), factor(n!)[, 2])); if(#e == 0, 0, vecmax(e)); }
(Python)
from collections import Counter
from sympy import factorint
def A375850(n): return max(filter(lambda x: x&1^1, sum((Counter(factorint(i)) for i in range(2, n+1)), start=Counter()).values()), default=0) # Chai Wah Wu, Aug 31 2024

Crossrefs

Cf. A000142, A001969, A011371, A125592, A375033, A375849.

Sequence in context: A373822 A021230 A273278 * A213089 A246644 A339703

Adjacent sequences: A375847 A375848 A375849 * A375851 A375853 A375854

Keyword

nonn,easy

Author

Amiram Eldar, Aug 31 2024

Status

approved