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A362401 Numbers in the range of A162296, where A162296(n) is the sum of divisors of n that have a square factor larger than 1.

%I A362401 #11 Apr 20 2023 13:20:26
%S A362401 0,4,9,12,16,24,25,27,28,32,36,48,49,54,56,60,72,75,79,80,96,100,108,
%T A362401 112,117,120,121,124,126,128,144,147,150,152,162,168,169,176,180,183,
%U A362401 192,196,199,200,216,224,240,248,252,268,270,272,288,289,294,296,300
%N A362401 Numbers in the range of A162296, where A162296(n) is the sum of divisors of n that have a square factor larger than 1.
%C A362401 Possible values of A162296 in increasing order.
%H A362401 Amiram Eldar, <a href="/A362401/b362401.txt">Table of n, a(n) for n = 1..10000</a>
%e A362401 0 is a term since A162296(k) = 0 if k is squarefree (A005117).
%t A362401 s[n_] := Module[{f = FactorInteger[n], p, e}, p = f[[;; , 1]]; e = f[[;; , 2]]; Times @@ ((p^(e + 1) - 1)/(p - 1)) - Times @@ (p + 1)]; s[1] = 0; m = 300; Select[Union[Array[s, m]], # <= m &]
%o A362401 (PARI) s(n) = {my(f = factor(n), p, e); prod(i = 1, #f~, p = f[i, 1]; e = f[i, 2]; ((p^(e + 1) - 1)/(p - 1))) -  prod(i = 1, #f~, f[i, 1] + 1);}
%o A362401 lista(kmax) = select(x -> (x < kmax), Set(vector(kmax, k, s(k))))
%Y A362401 Cf. A005117, A162296.
%Y A362401 Similar sequences: A078923, A002191, A002202, A002174, A274790.
%K A362401 nonn
%O A362401 1,2
%A A362401 _Amiram Eldar_, Apr 18 2023