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 A058008 #50 Sep 01 2025 12:23:35 %S A058008 1,6,15,28,42,45,66,77,91,110,126,140,153,156,170,187,190,204,209,210, %T A058008 220,228,231,238,266,276,299,308,312,315,322,325,330,345,378,414,420, %U A058008 429,435,440,442,450,459,460,468,476,483,493,496,510,527,551,558,561,570 %N A058008 Numbers k such that (2*k - 1)!/(k!)^2 is an integer. %C A058008 Original name was: Numbers n such that gcd(2*n,C(2*n,n))=2*n. %C A058008 For n a prime power (see A000961) we have gcd(2*n,C(2*n,n))=2. - _Arkadiusz Wesolowski_, Jul 01 2012 %C A058008 Also, positions where A075055 differs from A000984. - _Ralf Stephan_, Dec 11 2004 %C A058008 From _Peter Bala_, Aug 21 2025: (Start) %C A058008 Also numbers k such that (2*k - 2)!/(k!)^2 is an integer (since (2*k - 1)!/(k!)^2 + (2*k - 2)!/(k!)^2 = 2*Catalan(k-1) for k >= 1). Equivalently, numbers k such that Catalan(k-1) is divisible by k. %C A058008 Since for prime p, Catalan(p-1) == -1 (mod p), the entries in this list are all nonprime. (End) %H A058008 Giovanni Resta, <a href="/A058008/b058008.txt">Table of n, a(n) for n = 1..10000</a> %F A058008 Appears to be A067348(n)/2. - _Benoit Cloitre_, Mar 21 2003 %F A058008 Terms >1 are given by A002503+1. - _Benoit Cloitre_, Dec 09 2017 %p A058008 q:= k-> is(denom((2*k-1)!/(k!)^2)=1): %p A058008 select(q, [$1..600])[]; # _Alois P. Heinz_, Feb 06 2025 %t A058008 Select[Range[500], IntegerQ[(2 # - 1)!/#!^2] &] (* _Arkadiusz Wesolowski_, Jul 01 2012 *) %Y A058008 Cf. A000108, A000961, A001405, A002503, A075055, A000984, A067348. %K A058008 nonn,changed %O A058008 1,2 %A A058008 _Labos Elemer_, Nov 13 2000 %E A058008 Name changed by _Arkadiusz Wesolowski_, Jul 01 2012