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Search: id:A092975
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| A092975 |
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Consider all partitions of n into parts all of which are divisors of n; a(n) = maximal product of parts. |
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3
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| 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)
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OFFSET
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1,2
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COMMENT
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a(p) =p, a(p*q) = max(p^q, q^p). p,q are primes.
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FORMULA
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a(n) = Max{(n/d)^d : d divides n }. - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 06 2005
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EXAMPLE
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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.
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MATHEMATICA
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Table[ Max[(n/Divisors[n])^Divisors[n]], {n, 1, 100}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 23 2006
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CROSSREFS
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Sequence in context: A130064 A068795 A072501 this_sequence A164340 A046021 A052270
Adjacent sequences: A092972 A092973 A092974 this_sequence A092976 A092977 A092978
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Mar 27 2004
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 06 2005
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