A372601 The maximal exponent in the prime factorization of the largest exponentially odd divisor of n.

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

Offset

1,8

Comments

First differs from A331273 at n = 64.

Differs from A363332 at n = 1, 216, 432, 648, 864, 1000, ... .

Links

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

Formula

a(n) = A051903(A350390(n)).

a(n) = A109613(A051903(n)-1) for n >= 2.

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1 + 2 * Sum_{i>=1} (1 - (1/zeta(2*i+1))) = 1.42929441950714075659... .

Mathematica

f[n_] := n - If[EvenQ[n], 1, 0]; a[n_] := f[Max[FactorInteger[n][[;; , 2]]]]; a[1] = 0; Array[a, 100]

Prog

(PARI) s(n) = (n+1) \ 2 * 2 - 1;
a(n) = if(n>1, s(vecmax(factor(n)[, 2])), 0);

Crossrefs

Cf. A051903, A109613, A350390, A368711.

Cf. A331273, A363332.

Similar sequences: A007424, A368781, A372602, A372603, A372604.

Sequence in context: A372604 A331273 A363332 * A333843 A339876 A204129

Adjacent sequences: A372598 A372599 A372600 * A372602 A372603 A372604

Keyword

nonn,easy

Author

Amiram Eldar, May 07 2024

Status

approved