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Search: id:A130776
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| A130776 |
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Numbers n such that the sum of the proper divisors of n and n+1 equals either n or n+1. |
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+0
1
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| 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; listen)
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OFFSET
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1,2
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics./.
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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CROSSREFS
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Sequence in context: A096477 A039059 A073639 this_sequence A077292 A036413 A069912
Adjacent sequences: A130773 A130774 A130775 this_sequence A130777 A130778 A130779
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KEYWORD
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nonn
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AUTHOR
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J. M. Bergot (thekingfishb(AT)yahoo.ca), Jul 14 2007
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EXTENSIONS
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Edited, corrected and extended by Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Jul 16 2007
a(29) - a(32) from Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 27 2007
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