A275996 Numbers n whose abundance is 64: sigma(n) - 2n = 64.

108, 220, 6808, 8968, 14008, 24448, 66928, 552568, 786208, 1020568, 5303488, 8229568, 10001848, 133685248, 499722448, 2608895488, 4733164768, 7163795488, 13707973408, 14468025568, 16122444736, 27339731968, 34351218688, 34672397728, 35371084288, 69657461248

Offset: 1

Author

Timothy L. Tiffin, Aug 16 2016

Keywords

• nonn
• changed

Comments

Any term x = a(m) of this sequence can be used with any term y of A275997 to satisfy the property (sigma(x)+sigma(y))/(x+y) = 2, which is a necessary (but not sufficient) condition for two numbers to be amicable.

The smallest amicable pair is (220, 284) = (a(2), A275997(2)) = (A063990(1), A063990(2)), where 284 - 220 = 64 is the abundance of 220 and the deficiency of 284.

The amicable pair (66928, 66992) = (a(7), A275997(11)) = (A063990(18), A063990(19)), and 66992 - 66928 = 64 is the abundance of 66928 and the deficiency of 66992.

Examples

			a(1) = 108, since sigma(108) - 2*108 = 280 - 216 = 64.
		

Links

• Max Alekseyev, Table of n, a(n) for n = 1..63

Crossrefs

Subsequence of A005101.

Cf. A002025, A063990, A275997, A088831, A088832, A088833, A141547, A175989, A275701, A066539, A259180.

Programs

PARI

isok(n) = sigma(n) - 2*n == 64; \\ Michel Marcus, Dec 30 2016

Extensions

a(14)-a(15) from Michel Marcus, Dec 30 2016

a(16)-a(21) from Lars Blomberg, Jan 12 2017

Terms a(22) onward from Max Alekseyev, Aug 27 2025