A265310 Least positive k such that the product of divisors of n (A007955) divides k!.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 9, 13, 14, 10, 12, 17, 15, 19, 15, 14, 22, 23, 16, 15, 26, 15, 21, 29, 20, 31, 16, 22, 34, 14, 21, 37, 38, 26, 20, 41, 28, 43, 33, 15, 46, 47, 24, 21, 25, 34, 39, 53, 27, 22, 28, 38, 58, 59, 25, 61, 62, 21, 24, 26, 44, 67, 51, 46, 28, 71, 27, 73

Offset

1,2

Comments

Conjecture: a(n) = n if and only if n is prime, 2*prime, 1, 8 or 9.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

A265310:= proc(n) local F, f, tau, a, p, k;
      F:= ifactors(n)[2];
      tau:= mul(1+f[2], f=F);
      k:= 1;
      for f in F do
        a:= f[2]*tau/2;
        p:= f[1];
        while add(floor(k/p^j), j=1..ilog[p](k)) < a do k:= p*(1+floor(k/p)) od;
      od;
      k
end proc:
map(A265310, [$1..100]); # Robert Israel, Dec 07 2015

Mathematica

Table[k = 1; While[! Divisible[k!, Times @@ Divisors@ n], k++]; k, {n, 73}] (* Michael De Vlieger, Dec 06 2015 *)

Prog

(PARI) a007955(n) = if(issquare(n, &n), n^numdiv(n^2), n^(numdiv(n)/2));
a(n) = {k=1; while(k, if(k! % a007955(n)==0, return(k)); k++)}
vector(100, n, a(n)) \\ Altug Alkan, Dec 06 2015

Crossrefs

Cf. A007955.

Sequence in context: A327526 A121758 A121759 * A291576 A355221 A180613

Adjacent sequences: A265307 A265308 A265309 * A265311 A265312 A265313

Keyword

nonn

Author

Gionata Neri, Dec 06 2015

Status

approved