A076530 Numbers n such that sigma(n) = sigma(n+1) - sigma(n-1).

2, 3, 23, 1967, 3263, 5015, 60455, 1016507, 4420163, 12055511, 14365607, 25726727, 27896423, 66562307, 72764735, 98734967, 175186655, 224868311, 253694927, 288657203, 386668343, 421575407, 504737747, 630645455, 1493547999

Offset: 1

Author

Joseph L. Pe, Oct 18 2002

Keywords

• nonn

Examples

			sigma(24) = 60. sigma(23) = 24. sigma(22) = 36 and 24 = 60 - 36; hence 23 is a term of the sequence.
		

Links

• Donovan Johnson and Giovanni Resta, Table of n, a(n) for n = 1..112 (terms < 10^13, first 50 terms from Donovan Johnson)

Crossrefs

Cf. A000203, A065900, A104149.

Programs

Mathematica

Select[Range[2, 10^5], DivisorSigma[1, # ] == DivisorSigma[1, # + 1] - DivisorSigma[1, # - 1] &]
Flatten[Position[Partition[DivisorSigma[1,Range[1493548000]],3,1],?(#[[2]] == #[[3]]-#[[1]]&),1,Heads->False]]+1 (* _Harvey P. Dale, Apr 13 2020 *)

Formula

a(n) = A065900(n) - 1 = A104149(n) + 1. - Alex Ratushnyak, Jul 06 2013

Extensions

a(8)-a(25) from Donovan Johnson, Feb 01 2009