A357493 Numbers k such that s(k) = 3*k, where s(k) is the sum of divisors of k that have a square factor (A162296).

480, 2688, 56304, 89400, 195216, 2095104, 9724032, 69441408, 1839272960, 5905219584

Offset: 1

Author

Amiram Eldar, Oct 01 2022

Keywords

• nonn
• more

Comments

Analogous to 3-perfect numbers (A005820) with nonsquarefree divisors.

Equivalently, numbers k such that A325314(k) = -2*k.

a(11) > 10^11, if it exists.

If k is one of the 6 known 3-perfect numbers, then 4*k is a term.

Examples

			480 is a term since A162296(480) = 1440 = 3*480.
		

Crossrefs

Cf. A162296, A325314.

Subsequence of A013929 and A068403.

Numbers k such that A162296(k) = m*k: A005117 (m=0), A001248 (m=1), A322609 (m=2), this sequence (m=3), A357494 (m=4).

Similar sequence: A005820.

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) == 3*n]; Select[Range[2, 10^7], q]