

A070982


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


10



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
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OFFSET

1,2


LINKS

Ivan Neretin, Table of n, a(n) for n = 1..10000
József Sándor, The sumofdivisors 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: A227470 A218396 A331926 * A275520 A187153 A213265
Adjacent sequences: A070979 A070980 A070981 * A070983 A070984 A070985


KEYWORD

nonn,look


AUTHOR

Benoit Cloitre, May 24 2002


STATUS

approved



