A357493 - OEIS

%I #9 Oct 01 2022 19:29:48

%S 480,2688,56304,89400,195216,2095104,9724032,69441408,1839272960,

%T 5905219584

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

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

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

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

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

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

%t 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]

%Y Cf. A162296, A325314.

%Y Subsequence of A013929 and A068403.

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

%Y Similar sequence: A005820.

%K nonn,more

%O 1,1

%A _Amiram Eldar_, Oct 01 2022