cp's OEIS Frontend

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.

%I A357496 #12 Oct 03 2022 04:11:09
%S A357496 1136,11696,22256,25472,43424,73664,131355,304336,267968,492608,
%T A357496 612704,674920,640305,788697,691292,705344,723392,813728,809776,
%U A357496 1117395,1258335,1559696,1518570,1598368,1821376,2218250,2058944,2678752,2744288,2765024,2848864,2610656,3134224
%N 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.
%C A357496 Analogous to amicable numbers (A002025 and A002046) with nonsquarefree divisors.
%C A357496 The terms are ordered according to their lesser counterparts (A357495).
%C A357496 Both members of each pair are necessarily nonsquarefree numbers.
%H A357496 Amiram Eldar, <a href="/A357496/b357496.txt">Table of n, a(n) for n = 1..1000</a>
%e A357496 1136 is a term since s(1136) = 880 and s(880) = 1136.
%t A357496 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
%Y A357496 Cf. A162296, A325314, A322609, A357493, A357494, A357495.
%Y A357496 Subsequence of A013929.
%Y A357496 Similar sequences: A002046, A002953, A126166, A126170, A259039, A292981, A322542, A324709, A348344.
%K A357496 nonn
%O A357496 1,1
%A A357496 _Amiram Eldar_, Oct 01 2022