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 A381314 #8 Feb 21 2025 08:15:26
%S A381314 4,9,25,49,72,108,121,144,169,200,288,289,324,361,392,400,500,529,576,
%T A381314 675,784,800,841,961,968,972,1125,1152,1323,1352,1369,1372,1568,1600,
%U A381314 1681,1849,1936,2025,2209,2304,2312,2500,2704,2809,2888,2916,3087,3136,3200
%N A381314 Powerful numbers that have a single exponent in their prime factorization that equals 2.
%C A381314 Number of the form A036966(m)/p, m >= 2, where p is a prime divisor of A036966(m).
%H A381314 Amiram Eldar, <a href="/A381314/b381314.txt">Table of n, a(n) for n = 1..10000</a>
%F A381314 Sum_{n>=1} 1/a(n) = Sum_{p prime}((p-1)/(p^3-p^2+1)) * Product_{p prime} (1 + 1/(p^2*(p-1))) = 0.53045141423939736076... .
%t A381314 With[{max = 3200}, Select[Union@ Flatten@ Table[i^2 * j^3, {j, 1, max^(1/3)}, {i, 1, Sqrt[max/j^3]}], Count[FactorInteger[#][[;; , 2]], 2] == 1 &]]
%o A381314 (PARI) isok(k) = if(k == 1, 0, my(e = factor(k)[, 2]); vecmin(e) > 1 && #select(x -> (x==2), e) == 1);
%Y A381314 Subsequence of A001694, A377816 and A377818.
%Y A381314 Subsequences: A001248, A143610, A179646, A179689, A179699, A189988, A189990, A190106, A190115, A190470, A190471.
%Y A381314 Cf. A036966, A065483.
%K A381314 nonn,easy
%O A381314 1,1
%A A381314 _Amiram Eldar_, Feb 19 2025