The On-Line Encyclopedia of Integer Sequences (OEIS)

A374327 revision #3

A374327

The maximal exponent in the prime factorization of the numbers whose maximal exponent in their prime factorization is a power of 2.

1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 4, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 4, 2, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 4, 4, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 2

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OFFSET

1,3

COMMENTS

First differs from {A369933(n+1), n>=1} at n = 378.

The first occurrence of 2^k, for k = 0, 1, ..., is at 1, 3, 14, 224, 57307, ..., which is the position of 2^(2^k) at A369938.

LINKS

Table of n, a(n) for n=1..87.

FORMULA

a(n) = 2^A374328(n).

a(n) = A051903(A369938(n)).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=0} 2^k * d(k) / Sum_{k>=0} d(k) = 1.41151462942556759486..., where d(k) = 1/zeta(2^k+1) - 1/zeta(2^k) for k>=1, and d(0) = 1/zeta(2).

MATHEMATICA

f[n_] := Module[{e = If[n == 1, 0, Max[FactorInteger[n][[;; , 2]]]]}, If[e == 2^IntegerExponent[e, 2], e, Nothing]]; Array[f, 150]

PROG

(PARI) lista(kmax) = {my(e); for(k = 2, kmax, e = vecmax(factor(k)[, 2]); if(e >> valuation(e, 2) == 1, print1(e, ", "))); }

CROSSREFS

Cf. A051903, A369933, A369938.

Similar sequences: A374324, A374325, A374326, A374328.

Sequence in context: A305393 A259154 A369933 * A368473 A106035 A293811

Adjacent sequences: A374324 A374325 A374326 * A374328 A374329 A374330

KEYWORD

nonn,easy

AUTHOR

Amiram Eldar, Jul 04 2024

STATUS

editing