A070982 Smallest integer k such that n divides sigma(k).

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, 34, 12, 173, 24, 16, 21, 86, 67, 76, 22, 73, 37, 18, 27, 163, 20, 257, 43, 40, 137, 281, 33, 52, 149, 101, 63, 211, 34, 109, 28, 49, 173, 353, 24, 169, 48, 32, 93, 72, 86, 401

Offset: 1

Author

Benoit Cloitre, May 24 2002

Keywords

• nonn
• look

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000
• József Sándor, The sum-of-divisors minimum and maximum functions, Research Report Collection, Volume 8, Issue 1, 2005. See p. 3.

Crossrefs

Right diagonal of A074625.

Cf. A005179 (analog for number of divisors), A061026 (analog for Euler totient).

Programs

Mathematica

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 *)
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 *)

PARI

a(n)=my(s); while(sigma(s++)%n, ); s

Formula

a(n) = min( k : sigma(k) == 0 mod(n) ).

Sum(k=1, n, a(k)) seems to be asymptotic to c*n^2 with probably 1.1 < c < 1.2.

By Xylouris' form of Linnk's theorem, a(n) << n^5. Can this be improved? - Charles R Greathouse IV, Mar 09 2017