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

1,2

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.

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

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 *)

Prog

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

Crossrefs

Right diagonal of A074625.

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

Sequence in context: A218396 A368154 A331926 * A275520 A187153 A213265

Adjacent sequences: A070979 A070980 A070981 * A070983 A070984 A070985

Keyword

nonn,look

Author

Benoit Cloitre, May 24 2002

Status

approved