A072892 The 4-cycle of the n => sigma(n)-n process. sigma(n) is the sum of divisors of n. (A000203).

1264460, 1547860, 1727636, 1305184, 1264460

Offset

1,1

Comments

The two smallest members of sociable quadruples (1264460 and 2115324, see A090615) were found by the Canadian mathematician and educator Kenneth Dudley Fryer (1924-1984) in 1965 (Honsberger, 1970). These were the first aliquot cycles of length greater than 2 that were found since 1918 (see A072890 and A072891). They were rediscovered by Cohen (1970). - Amiram Eldar, Mar 24 2024

References

Ross Honsberger, Ingenuity in Mathematics, Mathematical Association of America, 1970.

Links

Table of n, a(n) for n=1..5.

Henri Cohen, On amicable and sociable numbers, Math. Comp., Vol. 24, No. 110 (1970), pp. 423-429.

Eric Weisstein's World of Mathematics, Sociable Numbers.

Wikipedia, Sociable number.

Formula

a(4+n) = a(n).

Mathematica

NestWhileList[DivisorSigma[1, #] - # &, 1264460, UnsameQ, All] (* Amiram Eldar, Mar 24 2024 *)

Crossrefs

Cf. A000203, A001065, A072890, A072891, A090615.

Sequence in context: A250596 A250825 A292217 * A090615 A222975 A180624

Adjacent sequences: A072889 A072890 A072891 * A072893 A072894 A072895

Keyword

fini,full,nonn

Author

Miklos Kristof, Jul 29 2002

Status

approved