A372602 The maximal exponent in the prime factorization of the largest square dividing n.

0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 4, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 4, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 2, 6, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 4, 4, 0, 0, 2, 0, 0, 0

Offset

1,4

Links

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

Formula

a(n) = A051903(A008833(n)).

a(n) = A052928(A051903(n)).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2 * Sum_{i>=1} (1 - (1/zeta(2*i))) = 0.98112786070359477197... .

Mathematica

f[n_] := 2 * Floor[n/2]; a[n_] := f[Max[FactorInteger[n][[;; , 2]]]]; a[1] = 0; Array[a, 100]

Prog

(PARI) s(n) = n \ 2 * 2;
a(n) = if(n>1, s(vecmax(factor(n)[, 2])), 0);

Crossrefs

Cf. A008833, A051903, A052928.

Similar sequences: A007424, A368781, A372601, A372603, A372604.

Sequence in context: A379012 A369309 A216228 * A374202 A291957 A143063

Adjacent sequences: A372599 A372600 A372601 * A372603 A372604 A372605

Keyword

nonn,easy

Author

Amiram Eldar, May 07 2024

Status

approved