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A357495 Lesser 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.

%I A357495 #10 Oct 03 2022 04:09:59
%S A357495 880,10480,20080,24928,42976,69184,110565,252080,267712,489472,566656,
%T A357495 569240,603855,626535,631708,687424,705088,741472,786896,904365,
%U A357495 1100385,1234480,1280790,1425632,1749824,1993750,2012224,2401568,2439712,2496736,2542496,2573344,2671856
%N A357495 Lesser 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.
%C A357495 Analogous to amicable numbers (A002025 and A002046) with nonsquarefree divisors.
%C A357495 The larger counterparts are in A357496.
%C A357495 Both members of each pair are necessarily nonsquarefree numbers.
%H A357495 Amiram Eldar, <a href="/A357495/b357495.txt">Table of n, a(n) for n = 1..1000</a>
%e A357495 880 is a term since s(880) = 1136 and s(1136) = 880.
%t A357495 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, n]], {n, 2, 3*10^6}]; seq
%Y A357495 Cf. A162296, A325314, A322609, A357493, A357494, A357496.
%Y A357495 Subsequence of A013929.
%Y A357495 Similar sequences: A002025, A002952, A126165, A126169, A259038, A292980, A322541, A324708, A348343.
%K A357495 nonn
%O A357495 1,1
%A A357495 _Amiram Eldar_, Oct 01 2022