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Search: id:A113791
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| A113791 |
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Let S(n)=Sigma(n)/2. Numbers n such that S(S(n))=n, 1/2-Sociable number of order 1 or 2. |
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2
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| 6, 12, 14, 28, 48, 62, 112, 124, 160, 189, 192, 254, 448, 496, 508, 1984, 2032, 8128, 12288, 16382, 28672, 32764, 126976, 131056, 196608, 262142, 458752, 520192, 524224, 524284, 786432, 1048574, 1835008, 2031616, 2097136, 2097148, 8126464
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OFFSET
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1,1
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COMMENT
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Almost all terms are of the form 2^m*M_k where M_k means the Mersenne prime 2^k-1. a(9)=2^5*5 and a(10)=3^3*7 are sporadic solutions. S(a(9))=a(10).
All numbers of the form (M_j+1)/2 M_k, where M_j and M_k are Mersenne primes, are in this sequence. - Robert G. Wilson v (rgwv(at)rgwv.com) and T. D. Noe (noe(AT)sspectra.com), Jan 21 2006
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LINKS
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Eric Weisstein's World of Mathematics, WathWorld
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MATHEMATICA
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Select[ Range@8323071, DivisorSigma[1, DivisorSigma[1, # ]/2] == 2# &] (* Robert G. Wilson v *)
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CROSSREFS
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Sequence in context: A105773 A079946 A118586 this_sequence A135763 A030659 A142338
Adjacent sequences: A113788 A113789 A113790 this_sequence A113792 A113793 A113794
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KEYWORD
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nonn
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AUTHOR
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Yasutoshi Kohmoto zbi74583(AT)boat.zero.ad.jp, Jan 21 2006
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(at)rgwv.com) and T. D. Noe (noe(AT)sspectra.com), Jan 21 2006
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