A372603 - OEIS

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A372603

The maximal exponent in the prime factorization of the powerful part of n.

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

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OFFSET

1,4

COMMENTS

First differs from A275812 at n = 36, and from A212172 at n = 37.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

Cf. A051903, A057521, A087156, A368710.

Cf. A013661, A033150, A059956.

Cf. A212172, A275812.

Similar sequences: A007424, A368781, A372601, A372602, A372604.

Sequence in context: A216226 A123391 A375339 * A212172 A275812 A280683

Adjacent sequences: A372600 A372601 A372602 * A372604 A372605 A372606

KEYWORD

nonn,easy

AUTHOR

Amiram Eldar, May 07 2024

STATUS

approved