A113791 Let S(n)=Sigma(n)/2. Numbers n such that S(S(n))=n, 1/2-Sociable number of order 1 or 2.

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

Offset: 1

Author

Yasutoshi Kohmoto, Jan 21 2006

Keywords

• nonn

Comments

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 and T. D. Noe, Jan 21 2006

Links

• Eric Weisstein's World of Mathematics, Sociable Numbers

Programs

Mathematica

Select[ Range@8323071, DivisorSigma[1, DivisorSigma[1, # ]/2] == 2# &] (* Robert G. Wilson v *)

Extensions

More terms from Robert G. Wilson v and T. D. Noe, Jan 21 2006