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
Examples
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
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)
- Shyam Sunder Gupta, Amicable Numbers, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 5, 159-183.
- Peter Hagis and Graham Lord, Quasi-amicable numbers, Math. Comp. 31 (1977), 608-611.
- David Moews, Augmented amicable pairs
- Jan Munch Pedersen, Tables of Aliquot Cycles
- Wikipedia, Betrothed numbers
Programs
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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 *) -
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
Extensions
Computed by Fred W. Helenius (fredh(AT)ix.netcom.com)
Extended by T. D. Noe, Dec 29 2011