A073500 Numbers k such that sigma(k) = sigma(k+1)+sigma(k-1).

954, 1300, 11142, 38214, 89484, 152154, 167784, 254136, 303280, 473316, 574716, 813920, 918080, 1307022, 2008360, 3676242, 9878244, 10368512, 12548754, 19411480, 22493262, 42413484, 77766486, 81513816, 157874000, 240828972

Offset: 1

Author

Benoit Cloitre, Aug 27 2002

Keywords

• nonn

Links

• Giovanni Resta, Table of n, a(n) for n = 1..170 (terms < 10^13, first 50 terms from Donovan Johnson)

Crossrefs

Cf. A000203 (sigma), A076528.

Programs

Mathematica

s1 = s2 = s3 = 0; Do[ s1 = s2; s2 = s3; s3 = DivisorSigma[1, n]; If[ s2 == s1 + s3, Print[n - 1]], {n, 1, 10^8}]

PARI

list(lim) = {my(s1 = 0, s2 = 0, s3); for(k = 1, lim, s3 = sigma(k); if(s2 == s1 + s3, print1(k-1, ", ")); s1 = s2; s2 = s3);} \\ Amiram Eldar, May 09 2025

Formula

a(n) = A076528(n)-1 - Alex Ratushnyak, Jul 06 2013.

Extensions

Edited and extended by Robert G. Wilson v, Oct 24 2002

a(25)-a(26) from Donovan Johnson, Feb 01 2009