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A375848
The maximum exponent in the prime factorization of the numbers whose maximum exponent in their prime factorization is an evil number (A374590).
1
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
1,2
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.
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]
PROG
(PARI) lista(kmax) = {my(e); print1(0, ", "); for(k = 2, kmax, e = vecmax(factor(k)[, 2]); if(!(hammingweight(e) % 2), print1(e, ", "))); }
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
Amiram Eldar, Aug 31 2024
STATUS
approved