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

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Index entries for sequences computed from exponents in factorization of n.

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

Cf. A001969, A051903, A374590.

Sequence in context: A376659 A084742 A242033 * A301738 A302387 A049613

Adjacent sequences: A375845 A375846 A375847 * A375849 A375850 A375851

Keyword

nonn,easy,base

Author

Amiram Eldar, Aug 31 2024

Status

approved