cp's OEIS Frontend

A374326 The square root of the maximal exponent in the prime factorization of the numbers whose maximal exponent in their prime factorization is a square.

%I A374326 #7 Jul 06 2024 05:28:43
%S A374326 0,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,
%T A374326 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%U A374326 1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1
%N A374326 The square root of the maximal exponent in the prime factorization of the numbers whose maximal exponent in their prime factorization is a square.
%C A374326 First differs from A369936 at n = 95.
%C A374326 The first occurrence of k = 0, 1, ... is at 1, 2, 12, 335, 42563, ..., which is the position of 2^(k^2) at A369937.
%H A374326 Amiram Eldar, <a href="/A374326/b374326.txt">Table of n, a(n) for n = 1..10000</a>
%F A374326 a(n) = sqrt(A374325(n)).
%F A374326 a(n) = sqrt(A051903(A369937(n))).
%F A374326 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=1} k * d(k) / Sum_{k>=1} d(k) = 1.06543556163434367736..., where d(k) = 1/zeta(k^2+1) - 1/zeta(k^2) for k>=2, and d(1) = 1/zeta(2).
%t A374326 f[n_] := Module[{s = Sqrt[If[n == 1, 0, Max[FactorInteger[n][[;; , 2]]]]]}, If[IntegerQ[s], s, Nothing]]; Array[f, 200]
%o A374326 (PARI) lista(kmax) = {my(e); print1(0, ", "); for(k = 2, kmax, e = vecmax(factor(k)[, 2]); if(issquare(e), print1(sqrtint(e), ", ")));}
%Y A374326 Cf. A051903, A369936, A369937.
%Y A374326 Similar sequences: A374324, A374325, A374327, A374328.
%K A374326 nonn,easy
%O A374326 1,12
%A A374326 _Amiram Eldar_, Jul 04 2024