A097018 a(n) is the least number such that sigma(a(n)) is divisible by the n-th prime.

3, 2, 8, 4, 43, 9, 67, 37, 137, 173, 16, 73, 163, 257, 281, 211, 353, 169, 401, 283, 256, 157, 331, 1024, 193, 1009, 617, 641, 653, 677, 64, 523, 547, 277, 1489, 1811, 313, 977, 1669, 691, 1789, 1447, 4201, 1543, 787, 397, 421, 1783, 907, 457, 3727, 1433, 3373

Offset: 1

Author

Labos Elemer, Aug 23 2004

Keywords

• nonn

Comments

Note that a(n) always exists, because sigma(2^(p-2)) = 2^(p-1)-1 is divisible by p for p>2 (by Fermat's little theorem), so there is always a candidate for a(n). Compare A227470, A272349. - N. J. A. Sloane, May 01 2016

Examples

			n=11: a(11)=16 is the least number x such that sigma(x) is divisible by the 11th prime, 31.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A000040, A272349, A227470.

Programs

Magma

sol:=[]; p:=PrimesUpTo(10000); for n in [1..53] do k:=2; while Max(PrimeDivisors(SumOfDivisors(k))) ne p[n] do k:=k+1; end while; sol[n]:=k; end for; sol; // Marius A. Burtea, Jun 05 2019

Mathematica

ln[n_]:=Module[{x=1,p=Prime[n]},While[!Divisible[DivisorSigma[ 1,x], p],x++];x]; Array[ln,60] (* Harvey P. Dale, Sep 07 2014 *)
Module[{nn=5000,ds},ds=DivisorSigma[1,Range[nn]];Table[Position[ds,?(Divisible[#,n]&),1,1],{n,Prime[Range[60]]}]]//Flatten (* Much faster than the first program *) (* _Harvey P. Dale, May 18 2018 *)

PARI

sigma_hunt(x)=local(n=0,g);while(n++,g=sigma(n);if(g%x,,return(n)));
for(x=1,50,print1(sigma_hunt(prime(x))", ")) /* Phil Carmody, Mar 01 2013 */