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 A162947 #36 Jul 16 2025 01:04:31
%S A162947 1,12,18,20,28,32,44,45,50,52,63,68,75,76,92,98,99,116,117,124,147,
%T A162947 148,153,164,171,172,175,188,207,212,236,242,243,244,245,261,268,275,
%U A162947 279,284,292,316,325,332,333,338,356,363,369,387,388,404,412,423,425,428
%N A162947 Numbers k such that the product of all divisors of k equals k^3.
%C A162947 Contains the terms of A054753 (products p*q^2 of a prime p and the square of a different prime q), 1, and p^5, where p is prime.
%C A162947 Numbers k such that k^2 is equal to the product of proper divisors of k. - _Juri-Stepan Gerasimov_, May 03 2011
%H A162947 Harvey P. Dale, <a href="/A162947/b162947.txt">Table of n, a(n) for n = 1..1000</a>
%H A162947 David A. Corneth, <a href="/A162947/a162947.gp.txt">PARI program</a>
%F A162947 {n: A007955(n) = A000578(n)}. - _R. J. Mathar_, Jul 19 2009
%F A162947 {1} UNION A030515. - _R. J. Mathar_, Jul 19 2009
%e A162947 18 is in the sequence because the product of its divisors is 1 * 2 * 3 * 6 * 9 * 18 = 18^3.
%t A162947 Select[Range[500], Surd[Times@@Divisors[#], 3] == # &] (* _Harvey P. Dale_, Mar 15 2017 *)
%t A162947 Join[{1},Select[Range[430],DivisorSigma[0,#]==6 &]] (* _Stefano Spezia_, Jul 14 2025 *)
%o A162947 (PARI) isok(n) = my(d = divisors(n)); prod(i=1, #d, d[i]) == n^3; \\ _Michel Marcus_, Feb 04 2014
%o A162947 (PARI) \\ See Corneth link
%o A162947 (Python)
%o A162947 from itertools import chain, count, islice
%o A162947 from sympy import divisor_count
%o A162947 def A162947_gen(): # generator of terms
%o A162947 return chain((1,),filter(lambda n:divisor_count(n)==6,count(2)))
%o A162947 A162947_list = list(islice(A162947_gen(),20)) # _Chai Wah Wu_, Jun 25 2022
%Y A162947 Cf. A111398, A030628. - _R. J. Mathar_, Jul 19 2009
%Y A162947 Cf. A008578 (product of divisors equals n), A007422 (product of divisors equals n^2).
%K A162947 nonn,easy
%O A162947 1,2
%A A162947 _Claudio Meller_, Jul 18 2009
%E A162947 Edited by _R. J. Mathar_, Jul 19 2009