cp's OEIS Frontend

A368168 The number of unitary divisors of n that are cubefull exponentially odd numbers (A335988).

%I A368168 #8 Dec 16 2023 09:01:35
%S A368168 1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,2,1,1,1,1,2,1,1,
%T A368168 1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,1,1,1,1,1,1,1,1,1,1,1,1,
%U A368168 1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%N A368168 The number of unitary divisors of n that are cubefull exponentially odd numbers (A335988).
%C A368168 First differs from A359411 and A367516 at n = 64.
%C A368168 Also, the number of unitary divisors of the largest unitary divisor of n that is a cubefull exponentially odd number (A368167).
%H A368168 Amiram Eldar, <a href="/A368168/b368168.txt">Table of n, a(n) for n = 1..10000</a>
%F A368168 a(n) = A034444(A368167(n)).
%F A368168 Multiplicative with a(p^e) = 2 if e is odd that is larger than 1, and 1 otherwise.
%F A368168 a(n) >= 1, with equality if and only if n is in A335275.
%F A368168 a(n) <= n, with equality if and only if n is in A335988.
%F A368168 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = zeta(2) * Product_{p prime} (1 - 1/p^2 + 1/p^3 - 1/p^4) = 1.12560687309375943599... .
%t A368168 f[p_, e_] := If[e == 1 || EvenQ[e], 1, 2]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A368168 (PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i, 2] == 1 || !(f[i, 2]%2), 1, 2));}
%Y A368168 Cf. A013661, A034444, A055076, A325837, A335275, A335988, A368167, A368169.
%Y A368168 Cf. A359411, A367516.
%K A368168 nonn,easy,mult
%O A368168 1,8
%A A368168 _Amiram Eldar_, Dec 14 2023