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

6, 28, 30, 140, 80, 200, 40, 224, 12, 234, 84, 270, 66, 308, 78, 364, 102, 476, 496, 114, 532, 240, 600, 138, 644, 120, 672, 150, 700, 174, 812, 135, 819, 186, 868, 864, 936, 222, 1036, 246, 1148, 60, 1170, 258, 1204, 282, 1316, 560, 1400, 318, 1484, 1488, 330

Offset

1,1

Comments

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.

By construction, no number can occur more than once in the sequence.

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.

If we were to "forget" to output the smallest member in each club, we would get instead A095301.

Oppositely, if we output the smallest members only, we get instead A259918.

It is not known whether the number 10 belongs to this sequence.

Links

Jeppe Stig Nielsen, Table of n, a(n) for n = 1..6000

Doyon Kim, Friends of 12, arXiv:1608.06834 [math.HO], 2016.

Jeffrey Ward, Does Ten Have a Friend?, arXiv:0806.1001 [math.NT], 2008.

Eric Weisstein's World of Mathematics, Friendly Pair

Wikipedia, Friendly number.

Prog

(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])))

Crossrefs

Cf. A050973, A259918, A095301, A014567, A074902.

Terms form a subset of A069059.

Sequence in context: A145551 A356410 A338125 * A083865 A185351 A272971

Adjacent sequences: A259914 A259915 A259916 * A259918 A259919 A259920

Keyword

nonn

Author

Jeppe Stig Nielsen, Jul 08 2015

Status

approved