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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).
5
480, 2688, 56304, 89400, 195216, 2095104, 9724032, 69441408, 1839272960, 5905219584
OFFSET
1,1
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.
EXAMPLE
480 is a term since A162296(480) = 1440 = 3*480.
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]
CROSSREFS
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.
Sequence in context: A199808 A253401 A327944 * A063870 A329536 A331768
KEYWORD
nonn,more
AUTHOR
Amiram Eldar, Oct 01 2022
STATUS
approved