cp's OEIS Frontend

A258079 Numbers x such that (-1)sigma(x) | sigma(x) - x, where (-1)sigma(x) is defined in A049060 and sigma(x) - x is the sum of the aliquot parts of x (A001065).

%I A258079 #20 Sep 11 2015 05:52:47
%S A258079 1,2,6,10,36,168,1098,1204,2840,19488,1881124,3105700,445577184,
%T A258079 105314212224,134633963520,2167649138304
%N A258079 Numbers x such that (-1)sigma(x) | sigma(x) - x, where (-1)sigma(x) is defined in A049060 and sigma(x) - x is the sum of the aliquot parts of x (A001065).
%C A258079 Ratio is equal to 1 for 2, 36, 1204, 2840, 1881124, 3105700, ...
%C A258079 a(17) > 10^13. - _Hiroaki Yamanouchi_, Sep 11 2015
%e A258079 (-1)sigma(1) = 1, sigma(1) - 1 = 1 - 1 = 0 and 0 / 1 = 0;
%e A258079 (-1)sigma(2) = 1, sigma(2) - 2 = 3 - 2 = 1 and 1 / 1 = 1;
%e A258079 (-1)sigma(36) = 55, sigma(36) - 36 = 91 - 36 = 55 and 55 / 55 = 1; etc.
%p A258079 with(numtheory): P:=proc(q) local a,b,i,j,n; for n from 1 to q do a:=ifactors(n)[2]:
%p A258079 b:=1; for i from 1 to nops(a) do b:=b*(-1+sum(a[i][1]^j,j=1..a[i][2])): od:
%p A258079 if type((sigma(n)-n)/b,integer) then print(n); fi; od; end: P(10^6);
%Y A258079 Cf. A001065, A049060, A258077.
%K A258079 nonn,more
%O A258079 1,2
%A A258079 _Paolo P. Lava_, May 19 2015
%E A258079 a(13)-a(16) from _Hiroaki Yamanouchi_, Sep 11 2015