This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A051177 #43 Aug 12 2024 01:27:20
%S A051177 1,2,3,124,158,342,693,1896,3853,4434,5273,8640,14850,17928,110516,
%T A051177 178984,274534
%N A051177 Perfectly partitioned numbers: numbers k that divide the number of partitions p(k).
%C A051177 Are there infinitely many perfectly partitioned numbers? Does there exist some k > 3 for which p(k) is a perfectly partitioned number?
%C A051177 No other terms below 10^8. - _Max Alekseyev_, May 19 2014
%C A051177 A probabilistic analysis suggests that there are infinitely many terms. - _Franklin T. Adams-Watters_, Oct 07 2018
%D A051177 Problem 2464, Journal of Recreational Mathematics 29(4), p. 304.
%D A051177 Solution to problem 2464 "Perfect Partitions", Journal of Recreational Mathematics 30(4), pp. 294-295, 1999-2000.
%H A051177 Carlos Rivera, <a href="https://www.primepuzzles.net/puzzles/puzz_1029.htm">Puzzle 1029. p that divides the number of partitions of p</a>, The Prime Puzzles and Problems Connection.
%e A051177 a(4) = 124 because p(124) = 2841940500 is divisible by 124.
%e A051177 a(7) = 693 because partition number of 693 is 43397921522754943172592795 = 693*62623263380598763596815.
%t A051177 Do[ If[ Mod[ PartitionsP@n, n] == 0, Print@n], {n, 250000}] (* _Robert G. Wilson v_ *)
%t A051177 Select[Range[275000],Divisible[PartitionsP[#],#]&] (* _Harvey P. Dale_, Aug 21 2013~ *)
%o A051177 (PARI) for(n=1,20000,if(numbpart(n)%n==0,print1(n,","))) \\ _Klaus Brockhaus_, Sep 06 2006
%Y A051177 Cf. A000041.
%Y A051177 Cf. A093952 = partition number A000041(n) mod n.
%Y A051177 Cf. A056848, A128836, A121015.
%K A051177 nonn,nice,hard,more
%O A051177 1,2
%A A051177 M.A. Muller (mam(AT)land.sun.ac.za)
%E A051177 More terms from _Don Reble_, Jul 26 2002