This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A263940 #11 May 16 2019 08:53:09 %S A263940 3,4,6,37,96,937,2760,393216 %N A263940 Numbers such that the product of the sum of their anti-divisors and the sum of the reciprocals of their anti-divisors is an integer. %C A263940 A066466 is a subset of this sequence. %C A263940 The sums are 1, 1, 1, 57, 1, 1457, 385, 1, ... %e A263940 Anti-divisors of 937 are 2, 3, 5, 15, 25, 75, 125, 375 and 625. Their sum is 1250 while the sum of their reciprocals is 1/2 + 1/3 + 1/5 + 1/15 + 1/25 + 1/75 + 1/125 + 1/375 + 1/625 = 1457/1250. Finally 1250 * 1457/1250 = 1457. %p A263940 with(numtheory); P:=proc(q) local a,b,k,n; %p A263940 for n from 3 to q do a:=0; b:=0; %p A263940 for k from 2 to n-1 do if abs((n mod k)-k/2)<1 then a:=a+k; b:=b+1/k; %p A263940 fi; od; if type(a*b,integer) then print(n); fi; od; end: P(10^4); %t A263940 f[n_] := Cases[Range[2, n - 1], _?(Abs[Mod[n, #] - #/2] < 1 &)]; Select[Range[3, 3000], IntegerQ@ Times[Total@ f@ #, Total[1/f@ #]] &] (* _Michael De Vlieger_, Nov 11 2015 *) %Y A263940 Cf. A066272, A066466, A263928. %K A263940 nonn %O A263940 1,1 %A A263940 _Paolo P. Lava_, Oct 30 2015