A372603 - OEIS

%I #8 May 08 2024 08:52:58

%S 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,

%T 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,

%U 0,0,0,3,0,0,2,2,0,0,0,4,4,0,0,2,0,0,0

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

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

%H Amiram Eldar, <a href="/A372603/b372603.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A051903(A057521(n)).

%F a(n) = A087156(A051903(n)).

%F 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... .

%t f[n_] := If[n == 1, 0, n]; a[n_] := f[Max[FactorInteger[n][[;; , 2]]]]; a[1] = 0; Array[a, 100]

%o (PARI) s(n) = if(n == 1, 0, n);

%o a(n) = if(n>1, s(vecmax(factor(n)[,2])), 0);

%Y Cf. A051903, A057521, A087156, A368710.

%Y Cf. A013661, A033150, A059956.

%Y Cf. A212172, A275812.

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

%K nonn,easy

%O 1,4

%A _Amiram Eldar_, May 07 2024