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

Author

Amiram Eldar, Aug 13 2024

Keywords

• nonn
• easy

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.

Crossrefs

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

Programs

Mathematica

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

PARI

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

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... .