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Search: id:A051177
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| A051177 |
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Perfectly partitioned numbers: numbers n such that n divides the number of partitions p(n) of n. |
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3
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| 1, 2, 3, 124, 158, 342, 693, 1896, 3853, 4434, 5273, 8640, 14850, 17928, 110516, 178984, 274534
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Are there infinitely many perfectly partitioned numbers? Does there exist some n for which p(n) is a perfectly partitioned number?
No other terms below 10^7. - Max Alekseyev (maxal(AT)cs.ucsd.edu), Jul 29 2008
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REFERENCES
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Journal of Recreational Mathematics, vol. 29, #4, pg 304, problem 2464.
Journal of Recreational Mathematics, vol. 30(4) 294-5 1999-2000, Soln. to prob.2464, "Perfect Partitions".
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EXAMPLE
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a(4) = 124 because p(124) = 2841940500 is divisible by 124.
a(7) = 693 because partition number of 693 is 43397921522754943172592795 = 693*62623263380598763596815.
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MATHEMATICA
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Do[ If[ Mod[ PartitionsP@n, n] == 0, Print@n], {n, 250000}] (* Robert G. Wilson v *)
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PROGRAM
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(PARI) for(n=1, 20000, if(numbpart(n)%n==0, print1(n, ", "))) - (Klaus Brockhaus, Sep 06 2006)
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CROSSREFS
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Cf. A000041.
Cf. A093952 = partition number A000041(n) mod n.
Cf. A128836, A121015.
Adjacent sequences: A051174 A051175 A051176 this_sequence A051178 A051179 A051180
Sequence in context: A041813 A065842 A065841 this_sequence A125674 A095841 A004865
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KEYWORD
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hard,nice,nonn
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AUTHOR
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M.A. Muller (MAM(AT)LAND.SUN.AC.ZA)
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EXTENSIONS
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More terms from Don Reble (djr(AT)nk.ca), Jul 26 2002
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