cp's OEIS Frontend

A325314 a(n) = n - A162296(n), where A162296(n) is the sum of divisors of n that have a square factor.

%I A325314 #18 Feb 22 2024 02:18:55
%S A325314 1,2,3,0,5,6,7,-4,0,10,11,-4,13,14,15,-12,17,-9,19,-4,21,22,23,-24,0,
%T A325314 26,-9,-4,29,30,31,-28,33,34,35,-43,37,38,39,-32,41,42,43,-4,-9,46,47,
%U A325314 -64,0,-25,51,-4,53,-54,55,-40,57,58,59,-36,61,62,-9,-60,65,66,67,-4,69,70,71,-111,73,74,-25,-4,77,78,79,-88,-36,82,83
%N A325314 a(n) = n - A162296(n), where A162296(n) is the sum of divisors of n that have a square factor.
%H A325314 Antti Karttunen, <a href="/A325314/b325314.txt">Table of n, a(n) for n = 1..16384</a>
%H A325314 Antti Karttunen, <a href="/A325314/a325314.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F A325314 a(n) = n - A162296(n).
%F A325314 a(n) = A033879(n) + A325313(n).
%F A325314 a(A228058(n)) = -A325320(n).
%F A325314 Sum_{k=1..n} a(k) ~ c * n^2, where c = 1 - zeta(2)/2 = 0.1775329665... . - _Amiram Eldar_, Feb 22 2024
%t A325314 Array[# - DivisorSigma[1, #] + Times @@ (1 + FactorInteger[#][[;; , 1]]) - Boole[# == 1] &, 83] (* _Michael De Vlieger_, Jun 06 2019, after _Amiram Eldar_ at A162296 *)
%o A325314 (PARI)
%o A325314 A162296(n) = sumdiv(n, d, d*(1-issquarefree(d)));
%o A325314 A325314(n) = (n - A162296(n));
%Y A325314 Cf. A013661, A033879, A162296, A228058, A325313, A325315, A325320.
%K A325314 sign
%O A325314 1,2
%A A325314 _Antti Karttunen_, Apr 21 2019