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A051177
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Perfectly partitioned numbers: numbers k that divide the number of partitions p(k).
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31
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1, 2, 3, 124, 158, 342, 693, 1896, 3853, 4434, 5273, 8640, 14850, 17928, 110516, 178984, 274534
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OFFSET
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1,2
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COMMENTS
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Are there infinitely many perfectly partitioned numbers? Does there exist some k > 3 for which p(k) is a perfectly partitioned number?
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REFERENCES
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Problem 2464, Journal of Recreational Mathematics 29(4), p. 304.
Solution to problem 2464 "Perfect Partitions", Journal of Recreational Mathematics 30(4), pp. 294-295, 1999-2000.
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LINKS
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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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Select[Range[275000], Divisible[PartitionsP[#], #]&] (* Harvey P. Dale, Aug 21 2013~ *)
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PROG
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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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KEYWORD
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nonn,nice,hard,more
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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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STATUS
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approved
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