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A291882 a(n) is the least number k such that sigma(k+n) = Sum_{j=1..i} sigma(d_j), where d_j are the divisors of k.

%I A291882 #17 Sep 30 2017 11:30:29
%S A291882 1,2,10,1183,4514,1179,38,3325,9,126855,290,261,18,6,1930,104771947,
%T A291882 344,58,326,117,270754,13875,32,45,32,74,70,38,18,21200761175,206,
%U A291882 1179,86,16,56,357,85,18,124,39948225,361,171,1118,63,122,38,30,239267,482,1367247
%N A291882 a(n) is the least number k such that sigma(k+n) = Sum_{j=1..i} sigma(d_j), where d_j are the divisors of k.
%C A291882 a(123) > 10^11. - _Giovanni Resta_, Sep 15 2017
%H A291882 Paolo P. Lava, <a href="/A291882/a291882.txt">Terms from a(1) to a(300) ('?' for unknown values)</a>
%e A291882 Divisors of 1183 are 1, 7, 13, 91, 169 and 1183: sigma(1) + sigma(7) + sigma(13) + sigma(91) + sigma(169) + sigma(1183)= 1 + 8 + 14 + 112 + 183 + 1464 = 1782 = sigma(1183+3) and 1183 is the least number to have this property.
%p A291882 with(numtheory): P:=proc(q) local a,b,j,k,n; for n from 0 to q do for k from 1 to q do
%p A291882 a:=divisors(k); b:=add(sigma(a[j]),j=1..nops(a));
%p A291882 if sigma(k+n)=b then print(k); break; fi; od; od; end: P(10^6);
%o A291882 (PARI) a(n) = my(k = 1); while(sigma(k+n) != sumdiv(k, d, sigma(d)), k++); k; \\ _Michel Marcus_, Sep 19 2017
%Y A291882 Cf. A000203, A066218.
%K A291882 nonn
%O A291882 0,2
%A A291882 _Paolo P. Lava_, Sep 05 2017
%E A291882 a(15), a(29), a(39), a(75), a(84), a(89), a(111) from _Giovanni Resta_, Sep 15 2017