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
KEYWORD
nonn,look
AUTHOR
Benoit Cloitre, May 24 2002
STATUS
approved