login
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
OFFSET
1,2
LINKS
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
KEYWORD
nonn,look
AUTHOR
Benoit Cloitre, May 24 2002
STATUS
approved