Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #30 Jan 05 2025 19:51:41
%S 114,594,1140,3608,4698,5940,6232,7704,9520,10744,12285,13500,41360,
%T 44772,46980,60858,62100,67095,67158,73360,79650,79750,105976,118500,
%U 141664,142310,177750,185368,193392,217840,241024,298188,308220,308992,356408,399200
%N Smaller of bi-unitary amicable pair.
%C Analogous to amicable numbers with bi-unitary sigma (A188999) instead of sigma (A000203).
%C Hagis found all the bi-unitary amicable pairs with smaller members below 10^6.
%C The larger members are in A292981.
%H Amiram Eldar, <a href="/A292980/b292980.txt">Table of n, a(n) for n = 1..6368</a> (all terms below 2*10^11, from David Moews' site).
%H Peter Hagis, Jr., <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/25-2/hagis.pdf">Bi-unitary amicable and multiperfect numbers</a>, Fibonacci Quarterly, Vol. 25, No. 2 (1987), pp. 144-150.
%H David Moews, <a href="http://djm.cc/amicable.html">Perfect, amicable and sociable numbers</a>.
%e 3608 is in the sequence since A188999(3608) - 3608 = 3952 and A188999(3952) - 3952 = 3608.
%t fun[p_,e_]:=If[Mod[e,2]==1,(p^(e+1)-1)/(p-1),(p^(e+1)-1)/(p-1)-p^(e/2)];
%t bsigma[n_] := If[n==1,1,Times @@ (fun @@@ FactorInteger[n])]; Do[s = bsigma[n]; If[s > 2 n && bsigma[s - n] == s, Print[n]],{n,1,10000}] (* _Amiram Eldar_, Sep 29 2018 *)
%Y Cf. A002025, A188999, A292981.
%K nonn,changed
%O 1,1
%A _Amiram Eldar_, Sep 27 2017