A003502 - OEIS

%I #33 Jul 24 2019 12:03:40

%S 48,140,1050,1575,2024,5775,8892,9504,62744,186615,196664,199760,

%T 266000,312620,526575,573560,587460,1000824,1081184,1139144,1140020,

%U 1173704,1208504,1233056,1236536,1279950,1921185,2036420,2102750,2140215,2171240,2198504,2312024

%N The smaller of a betrothed pair.

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

%H Giovanni Resta, <a href="/A003502/b003502.txt">Table of n, a(n) for n = 1..4122</a> (terms < 10^13, terms 1..1000 from Donovan Johnson, 1001..1126 from Amiram Eldar)

%H P. Hagis and G. Lord, <a href="https://doi.org/10.1090/S0025-5718-1977-0434939-3">Quasi-amicable numbers</a>, Math. Comp. 31 (1977), 608-611.

%H D. Moews, <a href="http://djm.cc/augmented.fmtlist">Augmented amicable pairs</a>

%H Jan Munch Pedersen, <a href="http://62.198.248.44/aliquot/tables.htm">Tables of Aliquot Cycles</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Betrothed_numbers">Betrothed numbers</a>

%e 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

%t 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 *)

%o (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

%Y Cf. A000203, A003503, A005276.

%K nonn,nice

%O 1,1

%A _Robert G. Wilson v_

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

%E Extended by _T. D. Noe_, Dec 29 2011