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A051177 Perfectly partitioned numbers: numbers n such that n divides the number of partitions p(n) of n. 4
1, 2, 3, 124, 158, 342, 693, 1896, 3853, 4434, 5273, 8640, 14850, 17928, 110516, 178984, 274534 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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 10^8. - Max Alekseyev, May 19 2014

REFERENCES

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.

LINKS

Table of n, a(n) for n=1..17.

EXAMPLE

a(4) = 124 because p(124) = 2841940500 is divisible by 124.

a(7) = 693 because partition number of 693 is 43397921522754943172592795 = 693*62623263380598763596815.

MATHEMATICA

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~ *)

PROG

(PARI) for(n=1, 20000, if(numbpart(n)%n==0, print1(n, ", "))) - (Klaus Brockhaus, Sep 06 2006)

CROSSREFS

Cf. A000041.

Cf. A093952 = partition number A000041(n) mod n.

Cf. A128836, A121015.

Sequence in context: A041813 A065842 A065841 * A258968 A125674 A180533

Adjacent sequences:  A051174 A051175 A051176 * A051178 A051179 A051180

KEYWORD

hard,nice,nonn,more,changed

AUTHOR

M.A. Muller (MAM(AT)LAND.SUN.AC.ZA)

EXTENSIONS

More terms from Don Reble, Jul 26 2002

STATUS

approved

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Last modified October 21 13:33 EDT 2017. Contains 293696 sequences.