|
Search: id:A092975
|
|
|
| A092975 |
|
Consider all partitions of n into parts all of which are divisors of n; a(n) = maximal product of parts. |
|
+0
3
|
|
| 1, 2, 3, 4, 5, 9, 7, 16, 27, 32, 11, 81, 13, 128, 243, 256, 17, 729, 19, 1024, 2187, 2048, 23, 6561, 3125, 8192, 19683, 16384, 29, 59049, 31, 65536, 177147, 131072, 78125, 531441, 37, 524288, 1594323, 1048576, 41, 4782969, 43, 4194304, 14348907
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
a(p) =p, a(p*q) = max(p^q, q^p). p,q are primes.
|
|
FORMULA
|
a(n) = Max{(n/d)^d : d divides n }. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Aug 06 2005
|
|
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 (stefan.steinerberger(AT)gmail.com), Apr 23 2006
|
|
CROSSREFS
|
Sequence in context: A130064 A068795 A072501 this_sequence A046021 A052270 A069117
Adjacent sequences: A092972 A092973 A092974 this_sequence A092976 A092977 A092978
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Mar 27 2004
|
|
EXTENSIONS
|
More terms from Vladeta Jovovic (vladeta(AT)Eunet.yu), Aug 06 2005
|
|
|
Search completed in 0.002 seconds
|
