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A286917 Numbers k such that there is an anti-divisor d of k satisfying sigma(d) = k.

%I A286917 #26 Aug 01 2020 01:16:58
%S A286917 3,4,13,32,40,60,121,364,1093,3200,3280,9841,15120,16380,29282,29524,
%T A286917 88573,91728,264992,265720,797161,2391484,7174453,21523360,40098240,
%U A286917 64570081,71495424,78427440,193690562,193710244,229909120,581130733,689727360,1743392200,5230176601
%N A286917 Numbers k such that there is an anti-divisor d of k satisfying sigma(d) = k.
%C A286917 As powers of 3 are in the sequence (larger than 1), the sequence is infinite. - _David A. Corneth_, Jul 20 2020
%F A286917 sigma(3^m) is in the sequence, as is sigma(3^m*(3^(m + 1) - 2)) for prime 3^(m + 1) - 2. - _David A. Corneth_, Jul 20 2020
%e A286917 Anti-divisors of 60 are 7, 8, 11, 17, 24, 40 and sigma(24) = 60.
%p A286917 with(numtheory): P:= proc(q) local a,k,n; for n from 3 to q do a:=[];
%p A286917 for k from 2 to n-1 do if abs((n mod k)-k/2)<1 then a:=[op(a),k]; fi; od;
%p A286917 for k from 1 to nops(a) do if n=sigma(a[k]) then print(n); break; fi; od;
%p A286917 od; end: P(10^4); # _Paolo P. Lava_, May 16 2017
%o A286917 (PARI) isok(n) = {ad = select(t->n%t && t<n, concat(concat(divisors(2*n-1), divisors(2*n+1)), 2*divisors(n))); for (k=1, #ad, if ((n % ad[k]) && (sigma(ad[k])== n), return (1)););} \\ _Michel Marcus_, May 20 2017
%Y A286917 Cf. A000203, A014224, A066272, A081756, A130799.
%K A286917 nonn
%O A286917 1,1
%A A286917 _Paolo P. Lava_, May 16 2017
%E A286917 More terms from _Michel Marcus_, May 20 2017
%E A286917 a(22)-a(26) from _Jinyuan Wang_, Jul 20 2020
%E A286917 a(27)-a(35) from _David A. Corneth_, Jul 20 2020