A372601 - OEIS

%I #11 May 08 2024 08:53:06

%S 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,

%T 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,

%U 1,1,1,3,1,1,1,1,1,1,1,3,3,1,1,1,1,1,1

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

%C First differs from A331273 at n = 64.

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

%H Amiram Eldar, <a href="/A372601/b372601.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%F 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... .

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

%o (PARI) s(n) = (n+1) \ 2 * 2 - 1;

%o a(n) = if(n>1, s(vecmax(factor(n)[,2])), 0);

%Y Cf. A051903, A109613, A350390, A368711.

%Y Cf. A331273, A363332.

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

%K nonn,easy

%O 1,8

%A _Amiram Eldar_, May 07 2024