A375360 The maximum exponent in the prime factorization of the smallest exponentially odd number that is divisible by n.

0, 1, 1, 3, 1, 1, 1, 3, 3, 1, 1, 3, 1, 1, 1, 5, 1, 3, 1, 3, 1, 1, 1, 3, 3, 1, 3, 3, 1, 1, 1, 5, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 3, 1, 1, 5, 3, 3, 1, 3, 1, 3, 1, 3, 1, 1, 1, 3, 1, 1, 3, 7, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 3, 3, 1, 1, 1, 5, 5, 1, 1, 3, 1, 1, 1, 3, 1, 3, 1, 3, 1, 1, 1, 5, 1, 3, 3, 3, 1, 1, 1, 3, 1

Offset

1,4

Comments

Differs from A365331 at n = 1, 36, 72, 100, ... .

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(A356191(n)).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1 + 2 * Sum{k>=1} (1 - 1/zeta(2*k)) = 1.98112786070359477197... .

Mathematica

a[n_] := Module[{e = FactorInteger[n][[;; , 2]]}, Max[(If[OddQ[#], #, # + 1]) & /@ e]]; a[1] = 0; Array[a, 100]

Prog

(PARI) a(n) = if(n == 1, 0, vecmax(apply(x -> if(x % 2, x, x+1), factor(n)[, 2])));

Crossrefs

Cf. A051903, A356191, A365331, A372601, A375359.

Sequence in context: A176187 A372288 A180683 * A365331 A214635 A166030

Adjacent sequences: A375357 A375358 A375359 * A375361 A375362 A375363

Keyword

nonn,easy

Author

Amiram Eldar, Aug 13 2024

Status

approved