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 A054412 #32 Jul 17 2025 14:48:47
%S A054412 1,4,27,72,108,192,800,1458,3125,5120,6272,12500,21600,30375,36000,
%T A054412 48600,77760,84375,114688,116640,121500,138240,169344,225000,247808,
%U A054412 337500,384000,395136,600000,653184,750141,823543,857304,979776,1384448,1474560,1500000
%N A054412 Numbers k such that, in the prime factorization of k, the product of exponents equals the product of prime factors.
%C A054412 For p prime, numbers of the form p^p satisfy the condition, hence A051674 is a subsequence. - _Michel Marcus_, May 19 2014
%C A054412 Also, numbers of the form p^q * q^p, with distinct primes p and q, satisfy the condition, hence A082949 is a subsequence. - _Bernard Schott_, Apr 11 2020
%H A054412 Rémy Sigrist, <a href="/A054412/b054412.txt">Table of n, a(n) for n = 1..10000</a>
%H A054412 Rémy Sigrist, <a href="/A054412/a054412.gp.txt">PARI program for A054412</a>
%e A054412 192 is included because 192 =2^6 *3^1 and 2*3 = 6*1.
%t A054412 peppfQ[n_]:=Module[{f=Transpose[FactorInteger[n]]},Times@@First[f] == Times@@Last[f]]; Select[Range[1.5*10^6],peppfQ] (* _Harvey P. Dale_, Oct 14 2015 *)
%o A054412 (PARI) isok(n) = my(f = factor(n)); prod(i=1, #f~, f[i,2]) == prod(i=1, #f~, f[i,1]); \\ _Michel Marcus_, May 19 2014
%o A054412 (PARI) \\ See Links section.
%Y A054412 Cf. A051674, A054411, A082949.
%K A054412 nonn
%O A054412 1,2
%A A054412 _Leroy Quet_, May 09 2000
%E A054412 More terms from _James Sellers_, May 23 2000
%E A054412 New name and three more terms from _Michel Marcus_, May 19 2014