A392280 The maximum exponent in the prime factorization of the smallest multiple of n whose prime factorization exponents are all powers of 2.

0, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 2, 1, 1, 1, 4, 1, 2, 1, 2, 1, 1, 1, 4, 2, 1, 4, 2, 1, 1, 1, 8, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 2, 1, 1, 4, 2, 2, 1, 2, 1, 4, 1, 4, 1, 1, 1, 2, 1, 1, 2, 8, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 2, 2, 1, 1, 1, 4, 4, 1, 1, 2, 1, 1, 1, 4, 1, 2

Offset

1,4

Comments

Differs from A368104 at n = 1, 32, 36, 64, 72, 96, ... .

Links

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

Formula

a(n) = A051903(A356194(n)).

a(n) = A062383(A051903(n)-1) for n >= 2.

a(n) = 2^A392281(n) for n >= 2.

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1 + Sum_{k>=0} 2^k*(1-1/zeta(2^k+1)) = 1.88686592737569231834... .

Mathematica

a[n_] := 2^Ceiling[Log2[Max[FactorInteger[n][[;; , 2]]]]]; a[1] = 0; Array[a, 100]

Prog

(PARI) s(n) = {my(e = logint(n, 2)); if(n == 1 << e, n, 1 << (e+1)); }
a(n) = if(n == 1, 0, s(vecmax(factor(n)[, 2])));

Crossrefs

Cf. A051903, A062383, A138302, A368104, A368781, A369933, A369938, A374327, A392281.

Sequence in context: A370771 A368106 A368104 * A104404 A351655 A351656

Adjacent sequences: A392277 A392278 A392279 * A392281 A392282 A392283

Keyword

nonn,easy

Author

Amiram Eldar, Jan 06 2026

Status

approved