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A372603
The maximal exponent in the prime factorization of the powerful part of n.
5
0, 0, 0, 2, 0, 0, 0, 3, 2, 0, 0, 2, 0, 0, 0, 4, 0, 2, 0, 2, 0, 0, 0, 3, 2, 0, 3, 2, 0, 0, 0, 5, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 2, 2, 0, 0, 4, 2, 2, 0, 2, 0, 3, 0, 3, 0, 0, 0, 2, 0, 0, 2, 6, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 2, 2, 0, 0, 0, 4, 4, 0, 0, 2, 0, 0, 0
OFFSET
1,4
COMMENTS
First differs from A275812 at n = 36, and from A212172 at n = 37.
LINKS
FORMULA
a(n) = A051903(A057521(n)).
a(n) = A087156(A051903(n)).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1 - 1/zeta(2) + Sum_{i>=2} (1 - 1/zeta(i)) = A033150 - A059956 = 1.09728403825134113562... .
MATHEMATICA
f[n_] := If[n == 1, 0, n]; a[n_] := f[Max[FactorInteger[n][[;; , 2]]]]; a[1] = 0; Array[a, 100]
PROG
(PARI) s(n) = if(n == 1, 0, n);
a(n) = if(n>1, s(vecmax(factor(n)[, 2])), 0);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, May 07 2024
STATUS
approved