OFFSET
1,1
COMMENTS
All terms are abundant (A005101). - S. I. Dimitrov, May 20 2026
REFERENCES
R. K. Guy, Unsolved Problems in Number Theory, B5.
Ross Honsberger, Ingenuity in Mathematics, Random House, 1970, pp. 112-113.
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
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
KEYWORD
nonn,nice
AUTHOR
EXTENSIONS
Computed by Fred W. Helenius (fredh(AT)ix.netcom.com)
Extended by T. D. Noe, Dec 29 2011
STATUS
approved
