cp's OEIS Frontend

A372603 The maximal exponent in the prime factorization of the powerful part of n.

%I A372603 #8 May 08 2024 08:52:58
%S A372603 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 A372603 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 A372603 0,0,0,3,0,0,2,2,0,0,0,4,4,0,0,2,0,0,0
%N A372603 The maximal exponent in the prime factorization of the powerful part of n.
%C A372603 First differs from A275812 at n = 36, and from A212172 at n = 37.
%H A372603 Amiram Eldar, <a href="/A372603/b372603.txt">Table of n, a(n) for n = 1..10000</a>
%F A372603 a(n) = A051903(A057521(n)).
%F A372603 a(n) = A087156(A051903(n)).
%F A372603 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 A372603 f[n_] := If[n == 1, 0, n]; a[n_] := f[Max[FactorInteger[n][[;; , 2]]]]; a[1] = 0; Array[a, 100]
%o A372603 (PARI) s(n) = if(n == 1, 0, n);
%o A372603 a(n) = if(n>1, s(vecmax(factor(n)[,2])), 0);
%Y A372603 Cf. A051903, A057521, A087156, A368710.
%Y A372603 Cf. A013661, A033150, A059956.
%Y A372603 Cf. A212172, A275812.
%Y A372603 Similar sequences: A007424, A368781, A372601, A372602, A372604.
%K A372603 nonn,easy
%O A372603 1,4
%A A372603 _Amiram Eldar_, May 07 2024