A375849 The maximum odd exponent in the prime factorization of n!.

1, 1, 3, 3, 1, 1, 7, 7, 1, 1, 5, 5, 11, 11, 15, 15, 3, 3, 1, 9, 19, 19, 3, 3, 23, 23, 25, 25, 7, 7, 31, 31, 15, 15, 17, 17, 35, 35, 9, 9, 39, 39, 41, 41, 21, 21, 3, 3, 47, 47, 49, 49, 3, 13, 53, 53, 27, 27, 9, 9, 57, 57, 63, 63, 31, 31, 31, 15, 67, 67, 11, 11

Offset

2,3

Comments

The sequence of indices of record values, 2, 4, 8, 14, 16, 22, 26, 28, 32, 38, ..., are the odious numbers (A000069) multiplied by 2 (A128309).

Links

Amiram Eldar, Table of n, a(n) for n = 2..10000

Index entries for sequences related to factorial numbers.

Formula

a(n) = A375032(n!).

max(a(n), A375850(n)) = A011371(n).

Mathematica

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

Prog

(PARI) a(n) = {my(e = select(x -> (x % 2), factor(n!)[, 2])); if(#e > 0, vecmax(e)); }
(Python)
from collections import Counter
from sympy import factorint
def A375849(n): return max(filter(lambda x: x&1, sum((Counter(factorint(i)) for i in range(2, n+1)), start=Counter()).values())) # Chai Wah Wu, Aug 31 2024

Crossrefs

Cf. A000069, A000142, A011371, A128309, A375032, A375850.

Sequence in context: A075772 A142157 A119608 * A364633 A333513 A196646

Adjacent sequences: A375846 A375847 A375848 * A375850 A375851 A375853

Keyword

nonn,easy

Author

Amiram Eldar, Aug 31 2024

Status

approved