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%I #28 Sep 09 2018 08:37:58
%S 1,3,2,3,8,5,4,7,10,19,43,6,9,12,8,21,67,10,37,19,20,43,137,14,149,45,
%T 34,12,173,24,16,21,86,67,76,22,73,37,18,27,163,20,257,43,40,137,281,
%U 33,52,149,101,63,211,34,109,28,49,173,353,24,169,48,32,93,72,86,401
%N Smallest integer k such that n divides sigma(k).
%H Ivan Neretin, <a href="/A070982/b070982.txt">Table of n, a(n) for n = 1..10000</a>
%H József Sándor, <a href="https://rgmia.org/papers/v8n1/art4.pdf">The sum-of-divisors minimum and maximum functions</a>, Research Report Collection, Volume 8, Issue 1, 2005. See p. 3.
%F a(n) = min( k : sigma(k) == 0 mod(n) ).
%F Sum(k=1, n, a(k)) seems to be asymptotic to c*n^2 with probably 1.1 < c < 1.2.
%F By Xylouris' form of Linnk's theorem, a(n) << n^5. Can this be improved? - _Charles R Greathouse IV_, Mar 09 2017
%t a = ConstantArray[1, 67]; k = 1; While[Length[vac = Rest[Flatten[Position[a, 1]]]] > 0, k++; a[[Intersection[Divisors[DivisorSigma[1, k]], vac]]] *= k]; a (* _Ivan Neretin_, May 15 2015 *)
%t With[{dsk=Table[{k,DivisorSigma[1,k]},{k,500}]},Table[SelectFirst[ dsk, Divisible[#[[2]],n]&],{n,70}]][[All,1]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jan 04 2018 *)
%o (PARI) a(n)=my(s); while(sigma(s++)%n, ); s
%Y Right diagonal of A074625.
%Y Cf. A005179 (analog for number of divisors), A061026 (analog for Euler totient).
%K nonn,look
%O 1,2
%A _Benoit Cloitre_, May 24 2002
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