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Numbers in the range of A162296, where A162296(n) is the sum of divisors of n that have a square factor larger than 1.
5

%I #11 Apr 20 2023 13:20:26

%S 0,4,9,12,16,24,25,27,28,32,36,48,49,54,56,60,72,75,79,80,96,100,108,

%T 112,117,120,121,124,126,128,144,147,150,152,162,168,169,176,180,183,

%U 192,196,199,200,216,224,240,248,252,268,270,272,288,289,294,296,300

%N 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 Possible values of A162296 in increasing order.

%H Amiram Eldar, <a href="/A362401/b362401.txt">Table of n, a(n) for n = 1..10000</a>

%e 0 is a term since A162296(k) = 0 if k is squarefree (A005117).

%t 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 (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 lista(kmax) = select(x -> (x < kmax), Set(vector(kmax, k, s(k))))

%Y Cf. A005117, A162296.

%Y Similar sequences: A078923, A002191, A002202, A002174, A274790.

%K nonn

%O 1,2

%A _Amiram Eldar_, Apr 18 2023