A051177
Perfectly partitioned numbers: numbers k that divide the number of partitions p(k).
Original entry on oeis.org
1, 2, 3, 124, 158, 342, 693, 1896, 3853, 4434, 5273, 8640, 14850, 17928, 110516, 178984, 274534
Offset: 1
M.A. Muller (mam(AT)land.sun.ac.za)
a(4) = 124 because p(124) = 2841940500 is divisible by 124.
a(7) = 693 because partition number of 693 is 43397921522754943172592795 = 693*62623263380598763596815.
- 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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Do[ If[ Mod[ PartitionsP@n, n] == 0, Print@n], {n, 250000}] (* Robert G. Wilson v *)
Select[Range[275000],Divisible[PartitionsP[#],#]&] (* Harvey P. Dale, Aug 21 2013~ *)
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for(n=1,20000,if(numbpart(n)%n==0,print1(n,","))) \\ Klaus Brockhaus, Sep 06 2006
A162468
Integers n such that A000009(n) (the number of partitions of n into distinct parts) == 1 (mod n).
Original entry on oeis.org
1, 2, 11, 22, 92, 149, 6919, 25517, 45339, 146635, 167903, 7461583, 14809123, 75788157, 80012043
Offset: 1
A121015
Numbers n such that partition number p(n) == 14 (mod n).
Original entry on oeis.org
1, 2, 8, 1402, 3579, 4111, 5289, 6383, 6467, 15146, 32141, 41910, 82849, 110088, 127531, 185114, 1320338, 1467242, 5739729, 22507473, 32494198
Offset: 1
Partition number of 8 is 22 = 1*8 + 14, hence 8 is a term.
Partition number of 1402 is 52435757789401123913939450130086135644 = 37400683159344596229628709079947315*1402 + 14, hence 1402 is a term.
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Do[ If[ Mod[ PartitionsP@n - 14, n] == 0, Print@n], {n, 731000}] (* Robert G. Wilson v, Sep 14 2006 *)
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for(n=1,200000,if((numbpart(n)-14)%n==0,print1(n,","))) \\ Klaus Brockhaus, Sep 07 2006
Edited, corrected and extended (a(1) to a(3), a(11) to a(16)) by
Klaus Brockhaus, Sep 07 2006
Original entry on oeis.org
1, 6, 156, 305, 484, 1219, 322733, 14343797, 58460571, 68355787
Offset: 1
A056872
Numbers k such that k | p(k) + q(k) where p(k) = partition numbers (A000041) and q(k) = partition numbers into distinct parts (A000009).
Original entry on oeis.org
1, 5, 25, 42, 133, 618, 643, 701, 1962, 8150, 147458, 168459, 356038, 415870, 536685, 637757, 1093612, 1207618, 3368325, 3470706, 23400631, 37621653
Offset: 1
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Do[ If[ Mod[ PartitionsP[ n ] + PartitionsQ[ n ], n ] == 0, Print[ n ] ], {n, 1, 8150} ]
A056873
Numbers k such that k | p(k) - q(k) where p(k) = partition numbers (A000041) and q(k) = partition numbers into distinct parts (A000009).
Original entry on oeis.org
1, 8, 11, 34, 310, 1688, 2307, 2708, 13988, 21315, 46739, 426378, 771476, 11762557, 18628390, 19841526, 24396168, 85110245
Offset: 1
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Do[ If[ Mod[ PartitionsP[n] - PartitionsQ[n], n] == 0, Print[n]], {n, 1, 14577}]
Showing 1-6 of 6 results.
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