cp's OEIS Frontend

A259917 All friendly numbers, with smallest member of each club listed just before the second-smallest one.

%I A259917 #17 Feb 16 2025 08:33:26
%S A259917 6,28,30,140,80,200,40,224,12,234,84,270,66,308,78,364,102,476,496,
%T A259917 114,532,240,600,138,644,120,672,150,700,174,812,135,819,186,868,864,
%U A259917 936,222,1036,246,1148,60,1170,258,1204,282,1316,560,1400,318,1484,1488,330
%N A259917 All friendly numbers, with smallest member of each club listed just before the second-smallest one.
%C A259917 Run through all natural numbers i = 1, 2, 3, ... in order, and record for each the abundancy index sigma(i)/i. When we reach an abundancy that has been seen before, output first the "old" number which had that abundancy (unless that number has already been output earlier), and output secondly the current i.
%C A259917 By construction, no number can occur more than once in the sequence.
%C A259917 Friendly numbers that are not smallest in their club, appear in increasing order. Friendly numbers that are smallest in their club, appear just before the second-smallest member.
%C A259917 If we were to "forget" to output the smallest member in each club, we would get instead A095301.
%C A259917 Oppositely, if we output the smallest members only, we get instead A259918.
%C A259917 It is not known whether the number 10 belongs to this sequence.
%H A259917 Jeppe Stig Nielsen, <a href="/A259917/b259917.txt">Table of n, a(n) for n = 1..6000</a>
%H A259917 Doyon Kim, <a href="http://arxiv.org/abs/1608.06834">Friends of 12</a>, arXiv:1608.06834 [math.HO], 2016.
%H A259917 Jeffrey Ward, <a href="http://arxiv.org/abs/0806.1001">Does Ten Have a Friend?</a>, arXiv:0806.1001 [math.NT], 2008.
%H A259917 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FriendlyPair.html">Friendly Pair</a>
%H A259917 Wikipedia, <a href="https://en.wikipedia.org/wiki/Friendly_number">Friendly number</a>.
%o A259917 (PARI) known=List(); for(i=1,10^5,a=sigma(i)/i; match=0; for(j=1,#known,if(known[j][1]==a,match=j;break())); if(match,old=known[match][2]; if(old,print1(old,", "); known[match]=[a,0]); print(i,","),listput(known,[a,i])))
%Y A259917 Cf. A050973, A259918, A095301, A014567, A074902.
%Y A259917 Terms form a subset of A069059.
%K A259917 nonn
%O A259917 1,1
%A A259917 _Jeppe Stig Nielsen_, Jul 08 2015