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

1,2

Comments

Possible values of A162296 in increasing order.

Links

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

Example

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

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 &]

Prog

(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))))

Crossrefs

Cf. A005117, A162296.

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

Sequence in context: A309134 A312858 A312859 * A045673 A292226 A225870

Adjacent sequences: A362398 A362399 A362400 * A362402 A362403 A362404

Keyword

nonn

Author

Amiram Eldar, Apr 18 2023

Status

approved