OFFSET
1,2
COMMENTS
a(p) = p, a(p*q) = max(p^q, q^p). p,q are primes.
For n>1, maximum among the numbers p^(n/p), where p is a prime factor of n (for minimum, see A243405). Upper bound (for any n): a(n) <= (3^(1/3))^n = A002581^n. - Stanislav Sykora, Jun 04 2014
LINKS
Stanislav Sykora, Table of n, a(n) for n = 1..2000
FORMULA
a(n) = Max{(n/d)^d : d divides n }. - Vladeta Jovovic, Aug 06 2005
When n=3m then a(n)=3^m; otherwise, a(n)=q^(n/q), q being the smallest prime factor of n. - Stanislav Sykora, Jun 04 2014
EXAMPLE
a(12)= 81, the partition into divisors are (12), (6+6),(6+4+2),...(4+4+4), (4+3+3+2), ..., (3+3+3+3), (2+2+2+2+2+2) etc. as 3^4=81 > 4*3*3*2=72 > 2^6 =64.
MATHEMATICA
Table[ Max[(n/Divisors[n])^Divisors[n]], {n, 1, 100}] (* Stefan Steinerberger, Apr 23 2006 *)
PROG
(PARI) A092975(n)={my(p); if(n==1, return(1));
if(n%3==0, return(3^(n/3)));
p = factor(n)[1, 1]; return (p^(n\p)); }
CROSSREFS
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Mar 27 2004
EXTENSIONS
More terms from Vladeta Jovovic, Aug 06 2005
STATUS
approved