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 A175180 #33 May 25 2024 09:13:10 %S A175180 5,265,13775,716035,9980583,37220045,1934726305 %N A175180 Numbers k such that k^2 + 2 is powerful in the sense of A001694. %C A175180 This sequence is infinite (F. Luca in De Koninck). %C A175180 The values of k^2 are a subset of A076445, so 23 terms of the sequence are known from there. - _R. J. Mathar_, Mar 05 2010 %C A175180 Together with 1, supersequence of A238799. - _Arkadiusz Wesolowski_, Mar 06 2014 %C A175180 From _Amiram Eldar_, Feb 23 2024: (Start) %C A175180 a(8) <= 100568547815. %C A175180 A041042(2*k) is a term for all k >= 0 (since 3^3 * A041043(n)^2 - A041042(n)^2 = -1 if n is odd and 2 if n is even). (End) %D A175180 Jean-Marie De Koninck, Ces nombres qui nous fascinent, Entry 265, p. 71, Ellipses, Paris, 2008. %H A175180 Jean-Marie De Koninck, <a href="https://bookstore.ams.org/view?ProductCode=MBK/64">Those Fascinating Numbers</a>, Amer. Math. Soc., 2009, page 66. %e A175180 5 is in the sequence because 5^2 + 2 = 3^3 is powerful. %e A175180 265 is in the sequence because 265^2 + 2 = 51^2*3^3 is powerful. %e A175180 13775 is in the sequence because 13775^2 + 2 = 2651^2 * 3^3 is powerful. %t A175180 q[n_] := AllTrue[FactorInteger[n^2+2][[;;, 2]], # > 1 &]; Select[Range[10^6], q] (* _Amiram Eldar_, Feb 23 2024 *) %o A175180 (PARI) is(n)=ispowerful(n^2+2) \\ _Charles R Greathouse IV_, Feb 04 2013 %Y A175180 Cf. A001694, A041042, A041043, A076445, A238799. %K A175180 nonn,hard,more %O A175180 1,1 %A A175180 _Michel Lagneau_, Mar 01 2010 %E A175180 Examples rephrased by _R. J. Mathar_, Feb 24 2010, Mar 05 2010 %E A175180 a(7) from _Amiram Eldar_, Feb 23 2024