A130776 Numbers n such that the sum of the proper divisors of n and n+1 equals either n or n+1.

1, 2, 3, 4, 6, 7, 16, 28, 31, 38, 127, 256, 278, 469, 1298, 3477, 7298, 7525, 8191, 13969, 19909, 26738, 31492, 65536, 99381, 131071, 357698, 524287, 20742482, 33550336, 772499089, 1959272066

Offset

1,2

Links

Table of n, a(n) for n=1..32.

Eric Weisstein's World of Mathematics, Aliquot Divisor.

Example

16 has the proper divisors 1,2,4 and 8. 17 has the proper divisor 1. The sum of those divisors is 16, therefore 16 is in the sequence.

Mathematica

Select[Range[1000000], DivisorSigma[1, # ] + DivisorSigma[1, # + 1] - 2*# - 1 == # || DivisorSigma[1, # ] + DivisorSigma[1, # + 1] - 2*# - 1 == # + 1 &]
lst = {}; d1 = d2 = 1; Do[ d2 = DivisorSigma[1, n + 1]; d = d1 + d2 - 2 n - 1; If[d == n || d == n + 1, Print@n; AppendTo[lst, n]]; d1 = d2, {n, 2*10^9}]; lst (* Robert G. Wilson v, Jul 27 2007 *)

Crossrefs

Sequence in context: A151892 A162570 A073639 * A077292 A270475 A171249

Adjacent sequences: A130773 A130774 A130775 * A130777 A130778 A130779

Keyword

nonn,more

Author

J. M. Bergot, Jul 14 2007

Extensions

Edited, corrected and extended by Stefan Steinerberger, Jul 16 2007

a(29)-a(32) from Robert G. Wilson v, Jul 27 2007

Status

approved