A050973 Larger member of friendly pairs ordered by smallest maximal element.

28, 140, 200, 224, 234, 270, 308, 364, 476, 496, 496, 532, 600, 644, 672, 700, 812, 819, 868, 936, 1036, 1148, 1170, 1204, 1316, 1400, 1484, 1488, 1488, 1540, 1638, 1638, 1638, 1652, 1708, 1800, 1820, 1876, 1988, 2016, 2044, 2200, 2212, 2324

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn

Comments

Perfect numbers greater than 6 (A000396) belong to this sequence as they form friendly pairs with smaller perfect, so that the n-th perfect number will appear n-1 times in the sequence. - Michel Marcus, Dec 03 2013

If we remove duplicates from the sequence we get A095301. - Jeppe Stig Nielsen, Jul 08 2015

It is possible to derive a friendly pair from 2 existing pairs (a_n,b_n) and (a_k,b_k); if (a_n,b_k) and (a_k,b_n) (resp. (a_k,b_k) and (a_n,b_n)) are coprime, then (a_n*b_k,a_k*b_n) (resp. (a_k*b_k,a_n*b_n)) is a friendly pair. For instance one can derive (32760,30240) from (819,135) and (224,40). Moreover, since 32760/35 and 30240/35 are both coprime to 35, one can also derive the primitive friendly pair (936,864). - Michel Marcus, Oct 09 2015

Links

• Donovan Johnson, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Friendly Pair.

Crossrefs

Cf. A050972, A074902, A095301.

Programs

PARI

lista(nn) = {for (n=1, nn, ab = sigma(n)/n; for (i=2, n-1, if (sigma(i)/i == ab, print1(n, ", "));););} \\ Michel Marcus, Dec 03 2013