A375848 - OEIS

%I #9 Aug 31 2024 15:16:28

%S 0,3,3,3,5,3,3,3,6,3,3,5,3,3,3,3,3,3,3,5,3,3,3,6,3,3,5,3,5,3,3,3,3,3,

%T 5,3,3,3,6,3,3,3,3,5,3,3,3,3,3,3,5,3,3,6,3,3,3,5,5,3,3,3,9,3,3,3,3,5,

%U 3,3,6,3,3,3,5,3,3,3,3,5,3,3,3,3,3,6,3,3,6,5,3,3,3,3,3,3,3,5,3,3,6,3,3,3,5

%N The maximum exponent in the prime factorization of the numbers whose maximum exponent in their prime factorization is an evil number (A374590).

%H Amiram Eldar, <a href="/A375848/b375848.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.

%F a(n) = A051903(A374590(n)).

%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k in A001969} (k * (1/zeta(k+1) - 1/zeta(k))) / d = 3.61461685523237846738..., where d = Sum_{k in A001969} (1/zeta(k+1) - 1/zeta(k)) = 0.12101890210392912747... is the asymptotic density of A374590.

%t evilQ[n_] := EvenQ[DigitCount[n, 2, 1]]; s[n_] := Module[{e = Max[FactorInteger[n][[;; , 2]]]}, If[evilQ[e], e, Nothing]]; s[1] = 0; Array[s, 1000]

%o (PARI) lista(kmax) = {my(e); print1(0, ", "); for(k = 2, kmax, e = vecmax(factor(k)[,2]); if(!(hammingweight(e) % 2), print1(e, ", ")));}

%Y Cf. A001969, A051903, A374590.

%K nonn,easy,base

%O 1,2

%A _Amiram Eldar_, Aug 31 2024