A243405 Minimum among the numbers p^(n/p), where p is a prime factor of n.

1, 2, 3, 4, 5, 8, 7, 16, 27, 25, 11, 64, 13, 49, 125, 256, 17, 512, 19, 625, 343, 121, 23, 4096, 3125, 169, 19683, 2401, 29, 15625, 31, 65536, 1331, 289, 16807, 262144, 37, 361, 2197, 390625, 41, 117649, 43, 14641, 1953125, 529, 47, 16777216, 823543, 9765625, 4913, 28561, 53

Offset

1,2

Comments

The setting a(1)=1 is conventional.

Upper bound (for any n): a(n) <= (3^(1/3))^n = A002581^n.

Links

Stanislav Sykora, Table of n, a(n) for n = 1..2000

Formula

For prime p, a(p)=p.

For n>1: When gpf(n)>3 then a(n)=gpf(n)^(n/gpf(n)); otherwise if n is even then a(n)=2^(n/2); otherwise a(n)=3^(n/3).

If n is in A033845, a(n) = 2^(n/2); otherwise a(n) = gpf(n)^(n/gpf(n)). - Franklin T. Adams-Watters, Jun 15 2014

Example

a(12)=64 because 2^(12/2)=64 is smaller than 3^(12/3)=81.

Prog

(PARI) A243405(n)= {my(m, k, p, q); if(n==1, return(1));
  p=factor(n); m=2^n;
  for(k=1, #p[, 1], q=p[k, 1]^(n\p[k, 1]); if(q<m, m=q));
  return (m); }

Crossrefs

Cf. A002581, A092975 (maximum instead of minimum), A033845.

Sequence in context: A069968 A298882 A086931 * A164339 A275465 A185198

Adjacent sequences: A243402 A243403 A243404 * A243406 A243407 A243408

Keyword

nonn

Author

Stanislav Sykora, Jun 04 2014

Status

approved