A357496 Greater of a pair of amicable numbers k < m such that s(k) = m and s(m) = k, where s(k) = A162296(k) - k is the sum of aliquot divisors of k that have a square factor.

1136, 11696, 22256, 25472, 43424, 73664, 131355, 304336, 267968, 492608, 612704, 674920, 640305, 788697, 691292, 705344, 723392, 813728, 809776, 1117395, 1258335, 1559696, 1518570, 1598368, 1821376, 2218250, 2058944, 2678752, 2744288, 2765024, 2848864, 2610656, 3134224

Offset: 1

Author

Amiram Eldar, Oct 01 2022

Keywords

• nonn

Comments

Analogous to amicable numbers (A002025 and A002046) with nonsquarefree divisors.

The terms are ordered according to their lesser counterparts (A357495).

Both members of each pair are necessarily nonsquarefree numbers.

Examples

			1136 is a term since s(1136) = 880 and s(880) = 1136.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A162296, A325314, A322609, A357493, A357494, A357495.

Subsequence of A013929.

Similar sequences: A002046, A002953, A126166, A126170, A259039, A292981, A322542, A324709, A348344.

Programs

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) - n]; seq = {}; Do[m = s[n]; If[m > n && s[m] == n, AppendTo[seq, m]], {n, 2, 3*10^6}]; seq