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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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4
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1, 2, 3, 124, 158, 342, 693, 1896, 3853, 4434, 5273, 8640, 14850, 17928, 110516, 178984, 274534
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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 3*10^7. - Max Alekseyev (maxale(AT)gmail.com), Jul 29 2008
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REFERENCES
| 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
| 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
| Do[ If[ Mod[ PartitionsP@n, n] == 0, Print@n], {n, 250000}] (* Robert G. Wilson v *)
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PROG
| (PARI) for(n=1, 20000, if(numbpart(n)%n==0, print1(n, ", "))) - (Klaus Brockhaus, Sep 06 2006)
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CROSSREFS
| Cf. A000041.
Cf. A093952 = partition number A000041(n) mod n.
Cf. A128836, A121015.
Sequence in context: A041813 A065842 A065841 * A125674 A180533 A095841
Adjacent sequences: A051174 A051175 A051176 * A051178 A051179 A051180
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KEYWORD
| hard,nice,nonn
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AUTHOR
| M.A. Muller (MAM(AT)LAND.SUN.AC.ZA)
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EXTENSIONS
| More terms from Don Reble (djr(AT)nk.ca), Jul 26 2002
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