OFFSET
1,1
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.
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved