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 A051177 Perfectly partitioned numbers: numbers n such that n divides the number of partitions p(n) of n. 11
 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 > 3 for which p(n) is a perfectly partitioned number? No other terms below 10^8. - Max Alekseyev, May 19 2014 A probabilistic analysis suggests that there are infinitely many terms. - Franklin T. Adams-Watters, Oct 07 2018 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 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. A056848, A128836, A121015. Sequence in context: A041813 A065842 A065841 * A334661 A258968 A125674 Adjacent sequences:  A051174 A051175 A051176 * A051178 A051179 A051180 KEYWORD hard,nice,nonn,more 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 September 27 03:21 EDT 2020. Contains 337380 sequences. (Running on oeis4.)