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A130776 Numbers n such that the sum of the proper divisors of n and n+1 equals either n or n+1. 0
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 (list; graph; refs; listen; history; text; internal format)
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 *)

CROSSREFS

Sequence in context: A151892 A162570 A073639 * A077292 A270475 A171249

Adjacent sequences:  A130773 A130774 A130775 * A130777 A130778 A130779

KEYWORD

nonn

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

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Last modified March 26 23:10 EDT 2019. Contains 321566 sequences. (Running on oeis4.)