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A375850
The maximum even exponent in the prime factorization of n!, or 0 if no such exponent exists.
2
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).
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
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Aug 31 2024
STATUS
approved