A275369 - OEIS

%I #25 Aug 16 2016 09:48:18

%S 1,3,3,5,5,8,14,19,19,23,23,30,30,31,50,50,50,50,50,51,51,64,90,90,91,

%T 91,91,91,126,130,130,130,130,130,130,130,130,130,131,132,132,132,132,

%U 132,134,134,234,234,234,234,236,236,236,236,288,288,288,288

%N Least k such that n! divides sigma(k!) (k > 0).

%H Robert Israel, <a href="/A275369/b275369.txt">Table of n, a(n) for n = 1..1100</a>

%e a(3) = 3 because 3! divides sigma(3!) = 12.

%p N:= 500: # to get a(1) .. a(N)

%p k:= 1; skf:= 1;

%p for n from 1 to N do

%p   nf:= n!;

%p   while skf mod nf <> 0 do

%p     k:= k+1;

%p     skf:= numtheory:-sigma(k!);

%p   od:

%p   A[n]:= k;

%p od:

%p seq(A[i],i=1..N); # _Robert Israel_, Aug 09 2016

%t Table[k = 1; While[! Divisible[DivisorSigma[1, k!], n!], k++]; k, {n, 58}] (* _Michael De Vlieger_, Aug 08 2016 *)

%o (PARI) a(n) = {my(k = 1); while(sigma(k!) % n! != 0, k++); k; }

%Y Cf. A000142, A062569.

%K nonn

%O 1,2

%A _Altug Alkan_, Jul 29 2016