|
|
A374328
|
|
The base-2 logarithm of the maximal exponent in the prime factorization of the numbers whose maximal exponent in their prime factorization is a power of 2.
|
|
5
|
|
|
0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 2, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,14
|
|
COMMENTS
|
First differs from {A369934(n+1), n>=1} at n = 378.
The first occurrence of k = 0, 1, ... is at 1, 3, 14, 224, 57307, ..., which is the position of 2^(2^k) at A369938.
|
|
LINKS
|
|
|
FORMULA
|
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=0} k * d(k) / Sum_{k>=0} d(k) = 0.35575339438419889972..., 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], IntegerExponent[e, 2], 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(valuation(e, 2), ", "))); }
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|