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A243405 Minimum among the numbers p^(n/p), where p is a prime factor of n. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A056240 A069968 A086931 * A164339 A275465 A185198

Adjacent sequences:  A243402 A243403 A243404 * A243406 A243407 A243408

KEYWORD

nonn

AUTHOR

Stanislav Sykora, Jun 04 2014

STATUS

approved

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Last modified July 24 21:38 EDT 2017. Contains 289777 sequences.