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 A009191 #40 Mar 31 2019 04:09:15 %S A009191 1,2,1,1,1,2,1,4,3,2,1,6,1,2,1,1,1,6,1,2,1,2,1,8,1,2,1,2,1,2,1,2,1,2, %T A009191 1,9,1,2,1,8,1,2,1,2,3,2,1,2,1,2,1,2,1,2,1,8,1,2,1,12,1,2,3,1,1,2,1,2, %U A009191 1,2,1,12,1,2,3,2,1,2,1,10,1,2,1,12,1,2,1,8,1,6,1,2,1,2,1,12,1,2,3,1,1,2,1,8,1 %N A009191 a(n) = gcd(n, d(n)), where d(n) is the number of divisors of n (A000005). %C A009191 a(A046642(n)) = 1. %C A009191 First occurrence of k: 1, 2, 9, 8, 400, 12, 3136, 24, 36, 80, 123904, 60, 692224, 448, 2025, 384, .... Conjecture: each k is present. - _Robert G. Wilson v_, Mar 27 2013 %C A009191 Conjecture is true. See _David A. Corneth_'s comment in A324553. - _Antti Karttunen_, Mar 06 2019 %H A009191 Antti Karttunen, <a href="/A009191/b009191.txt">Table of n, a(n) for n = 1..65537</a> (terms 1..1000 from T. D. Noe) %F A009191 a(n) = gcd(n, A000005(n)) = gcd(n, A049820(n)). - _Antti Karttunen_, Sep 25 2018 %t A009191 f[n_] := GCD[n, DivisorSigma[0, n]]; Array[f, 105] (* _Robert G. Wilson v_, Mar 27 2013 *) %o A009191 (Haskell) %o A009191 a009191 n = gcd n $ a000005 n %o A009191 -- _Reinhard Zumkeller_, May 09 2013, Aug 14 2011 %o A009191 (PARI) a(n)=gcd(numdiv(n),n) \\ _Charles R Greathouse IV_, Mar 26 2013 %Y A009191 Cf. A000005, A009194, A009195, A009205, A009213, A009230, A049820, A125168, A138010, A286540, A303781, A318459, A319337, A322979, A322980, A323073. %Y A009191 Cf. A046642 (positions of ones), A324553 (position of the first occurrence of each n). %K A009191 nonn %O A009191 1,2 %A A009191 _David W. Wilson_