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%I #16 Jun 07 2014 01:51:30
%S 1,2,3,4,5,9,7,16,27,32,11,81,13,128,243,256,17,729,19,1024,2187,2048,
%T 23,6561,3125,8192,19683,16384,29,59049,31,65536,177147,131072,78125,
%U 531441,37,524288,1594323,1048576,41,4782969,43,4194304,14348907
%N Consider all partitions of n into parts all of which are divisors of n; a(n) = maximal product of parts.
%C a(p) = p, a(p*q) = max(p^q, q^p). p,q are primes.
%C 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
%H Stanislav Sykora, <a href="/A092975/b092975.txt">Table of n, a(n) for n = 1..2000</a>
%F a(n) = Max{(n/d)^d : d divides n }. - _Vladeta Jovovic_, Aug 06 2005
%F 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
%e 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.
%t Table[ Max[(n/Divisors[n])^Divisors[n]], {n, 1, 100}] (* _Stefan Steinerberger_, Apr 23 2006 *)
%o (PARI) A092975(n)={my(p);if(n==1,return(1));
%o if(n%3==0,return(3^(n/3)));
%o p = factor(n)[1,1];return (p^(n\p));}
%Y Cf. A002581, A243405.
%K nonn
%O 1,2
%A _Amarnath Murthy_, Mar 27 2004
%E More terms from _Vladeta Jovovic_, Aug 06 2005
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