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

Author

Miklos Kristof, Jul 29 2002

Keywords

• fini
• full
• nonn

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

• 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.

Crossrefs

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

Programs

Mathematica

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

Formula

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