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.

0, 4, 9, 12, 16, 24, 25, 27, 28, 32, 36, 48, 49, 54, 56, 60, 72, 75, 79, 80, 96, 100, 108, 112, 117, 120, 121, 124, 126, 128, 144, 147, 150, 152, 162, 168, 169, 176, 180, 183, 192, 196, 199, 200, 216, 224, 240, 248, 252, 268, 270, 272, 288, 289, 294, 296, 300

Offset: 1

Author

Amiram Eldar, Apr 18 2023

Keywords

• nonn

Comments

Possible values of A162296 in increasing order.

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005117, A162296.

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

Programs

Mathematica

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 &]

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);}
lista(kmax) = select(x -> (x < kmax), Set(vector(kmax, k, s(k))))