A375848 The maximum exponent in the prime factorization of the numbers whose maximum exponent in their prime factorization is an evil number (A374590).

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, 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, 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

Offset: 1

Author

Amiram Eldar, Aug 31 2024

Keywords

• nonn
• easy
• base

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Index entries for sequences computed from exponents in factorization of n.

Crossrefs

Cf. A001969, A051903, A374590.

Programs

Mathematica

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]

PARI

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

Formula

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

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.