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%I #15 Feb 10 2017 20:17:17
%S 1,3,3,8,1,5,7,16,9,7,3,16,7,1,8,9,5,27,5,6,10,8,7,14,23,15,27,11,9,
%T 16,11,36,2,19,7,81,37,16,21,18,3,20,43,16,45,5,15,27,25,30,4,45,32,2,
%U 11,31,22,30,28,18,14,7,40,128,13,4,67,14,8,24,23,189,73,39,37,32,28,14,35,42,81,14,9,40,17,45
%N Least k > 0 such that sigma(n) divides sigma(n+k).
%H Altug Alkan, <a href="/A282255/b282255.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A069789(n) - n. - _Michel Marcus_, Feb 10 2017
%e a(4) = 8 because sigma(4) = 7 divides sigma(4 + 8) = 28 and 8 is the least positive number with this property.
%t Table[k = 1; While[! Divisible[DivisorSigma[1, n + k], DivisorSigma[1, n]], k++]; k, {n, 120}] (* _Michael De Vlieger_, Feb 10 2017 *)
%o (PARI) a(n) = my(k = 1); while (sigma(n+k) % sigma(n) != 0, k++); k;
%Y Cf. A000203, A069789.
%K nonn
%O 1,2
%A _Altug Alkan_, Feb 10 2017
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