A003502 The smaller of a betrothed pair.

48, 140, 1050, 1575, 2024, 5775, 8892, 9504, 62744, 186615, 196664, 199760, 266000, 312620, 526575, 573560, 587460, 1000824, 1081184, 1139144, 1140020, 1173704, 1208504, 1233056, 1236536, 1279950, 1921185, 2036420, 2102750, 2140215, 2171240, 2198504, 2312024

Offset

1,1

References

R. K. Guy, Unsolved Problems in Number Theory, B5.

Links

Giovanni Resta, Table of n, a(n) for n = 1..4122 (terms < 10^13, terms 1..1000 from Donovan Johnson, 1001..1126 from Amiram Eldar)

P. Hagis and G. Lord, Quasi-amicable numbers, Math. Comp. 31 (1977), 608-611.

D. Moews, Augmented amicable pairs

Jan Munch Pedersen, Tables of Aliquot Cycles

Wikipedia, Betrothed numbers

Example

48 is a term because sigma(48) - 48 - 1 = 124 - 48 - 1 = 75 and 48 < 75 and sigma(75) - 75 - 1 = 124 - 75 - 1 = 48. - David A. Corneth, Jan 24 2019

Mathematica

aapQ[n_] := Module[{c=DivisorSigma[1, n]-1-n}, c!=n&&DivisorSigma[ 1, c]-1-c == n]; Transpose[Union[Sort[{#, DivisorSigma[1, #]-1-#}]&/@Select[Range[2, 10000], aapQ]]] [[1]] (* Amiram Eldar, Jan 24 2019 after Harvey P. Dale at A007992 *)

Prog

(PARI) is(n) = m = sigma(n) - n - 1; if(m == 0 || n >= m, return(0)); n == sigma(m) - m - 1 \\ David A. Corneth, Jan 24 2019

Crossrefs

Cf. A000203, A003503, A005276.

Sequence in context: A260972 A244380 A260493 * A129428 A039496 A044380

Adjacent sequences: A003499 A003500 A003501 * A003503 A003504 A003505

Keyword

nonn,nice

Author

Robert G. Wilson v

Extensions

Computed by Fred W. Helenius (fredh(AT)ix.netcom.com)

Extended by T. D. Noe, Dec 29 2011

Status

approved