A357494 Numbers k such that s(k) = 4*k, where s(k) is the sum of divisors of k that have a square factor (A162296).

902880, 1534680, 361674720, 767685600, 4530770640, 4941414720, 5405788800, 5517818880, 16993944000, 20429240832, 94820077440

Offset: 1

Author

Amiram Eldar, Oct 01 2022

Keywords

• nonn
• more

Comments

Analogous to 4-perfect numbers (A027687) with nonsquarefree divisors.

Equivalently, numbers k such that A325314(k) = -3*k.

There are no numbers k below 10^11 such that A162296(k) = m*k for integers m > 4.

Examples

			902880 is a term since A162296(902880) = 3611520 = 4*902880.
		

Crossrefs

Cf. A162296, A325314.

Subsequence of A013929 and A023198.

Numbers k such that A162296(k) = m*k: A005117 (m=0), A001248 (m=1), A322609 (m=2), A357493 (m=3), this sequence (m=4).

Similar sequence: A027687.

Programs

Mathematica

q[n_] := Module[{f = FactorInteger[n], p, e}, p = f[[;; , 1]]; e = f[[;; , 2]]; Times @@ ((p^(e + 1) - 1)/(p - 1)) - Times @@ (p + 1) == 4*n]; Select[Range[2, 2*10^6], q]