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A258077 Numbers x such that (-1)sigma(x) | sigma(x), where (-1)sigma(x) is defined in A049060 and sigma(x) is the sum of the divisors of x (A000203).

%I A258077 #18 Nov 11 2019 09:27:00
%S A258077 1,2,3,6,14,15,30,35,42,70,78,105,190,210,348,357,418,570,714,812,910,
%T A258077 1045,1254,2090,2436,2730,3135,4060,4522,4674,5278,6270,9990,10659,
%U A258077 12180,12441,13566,14630,15834,16770,20026,21318,21978,23374,24244,24871,24882
%N A258077 Numbers x such that (-1)sigma(x) | sigma(x), where (-1)sigma(x) is defined in A049060 and sigma(x) is the sum of the divisors of x (A000203).
%H A258077 Amiram Eldar, <a href="/A258077/b258077.txt">Table of n, a(n) for n = 1..5000</a> (terms 1..100 from Paolo P. Lava)
%e A258077 (-1)sigma(1) = 1, sigma(1) = 1 and 1 / 1 = 1;
%e A258077 (-1)sigma(2) = 1, sigma(2) = 3 and 3 / 1 = 3;
%e A258077 (-1)sigma(35) = 24, sigma(35) = 48 and 48 / 24 = 2; etc.
%p A258077 with(numtheory): P:=proc(q) local a,b,i,j,n; for n from 1 to q do a:=ifactors(n)[2]:
%p A258077 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 A258077 if type(sigma(n)/b,integer) then print(n); fi; od; end: P(10^6);
%Y A258077 Cf. A000203, A049060, A258079.
%K A258077 nonn
%O A258077 1,2
%A A258077 _Paolo P. Lava_, May 19 2015