A375667 - OEIS

%I #7 Aug 23 2024 10:43:06

%S 0,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,

%T 1,1,1,1,1,1,2,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,1,1,1,1,1,1,1,1,1,

%U 1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,1,1,1,2,1,1,1,1,1,1,1,1

%N The maximum exponent in the prime factorization of the 5-rough numbers (A007310).

%H Amiram Eldar, <a href="/A375667/b375667.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A051903(A007310(n)).

%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1 + Sum_{k>=2} (1 - 1/((1-1/2^k) * (1-1/3^k) * zeta(k))) = 1.1034178389191320571029... .

%t a[n_] := Max[FactorInteger[6*Floor[n/2] - (-1)^n][[;; , 2]]]; a[1] = 0; Array[a, 100]

%o (PARI) a(n) = if(n == 1, 0, vecmax(factor(n\2*6-(-1)^n)[,2]));

%Y Cf. A007310, A051903, A375039, A375668.

%K nonn,easy

%O 1,9

%A _Amiram Eldar_, Aug 23 2024