cp's OEIS Frontend

A365333 The number of exponentially odd coreful divisors of the largest square dividing n.

%I A365333 #15 Sep 11 2023 07:38:37
%S A365333 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,
%T A365333 1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,3,1,1,1,1,
%U A365333 1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1
%N A365333 The number of exponentially odd coreful divisors of the largest square dividing n.
%C A365333 First differs from A043289, A053164, A063775, A203640 and A295658 at n = 64.
%C A365333 The number of squares dividing the largest exponentially odd divisor of n is A325837(n).
%C A365333 The sum of the exponentially odd divisors of the largest square dividing n is A365334(n). [corrected, Sep 08 2023]
%C A365333 The number of exponentially odd divisors of the largest square dividing n is the same as the number of squares dividing n, A046951(n). - _Amiram Eldar_, Sep 08 2023
%H A365333 Amiram Eldar, <a href="/A365333/b365333.txt">Table of n, a(n) for n = 1..10000</a>
%F A365333 a(n) = A325837(A008833(n)).
%F A365333 a(n) = 1 if and only if n is a biquadratefree number (A046100).
%F A365333 Multiplicative with a(p^e) = max(1, floor(e/2)).
%F A365333 Dirichlet g.f.: zeta(s) * zeta(4*s) * zeta(6*s) / zeta(12*s).
%F A365333 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 15015/(1382*Pi^2) = 1.100823... .
%t A365333 f[p_, e_] := Max[1, Floor[e/2]]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A365333 (PARI) a(n) = vecprod(apply(x -> max(1, x\2), factor(n)[, 2]));
%Y A365333 Cf. A008833, A046100, A046951, A325837, A365334.
%Y A365333 Cf. A043289, A053164, A063775, A203640, A295658.
%K A365333 nonn,easy,mult
%O A365333 1,16
%A A365333 _Amiram Eldar_, Sep 01 2023
%E A365333 Name corrected by _Amiram Eldar_, Sep 08 2023