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 A091361 #25 Feb 09 2019 11:11:57 %S A091361 1,2,3,9,15,21,27,33,39,45,51,57,63,69,75,81,87,93,99,105,111,117,123, %T A091361 129,135,141,147,153,159,165,171,177,183,189,195,201,207,213,219,225, %U A091361 231,237,243,249,255,261,267,273,279,285,291,297,303,309,315,321,327 %N A091361 Numbers n such that A001840(n) == 0 (mod n). %C A091361 Apart from 1 and 2 it is conjectured that the only values present are congruent to 3 mod 6 (all these values are present). %C A091361 From _R. J. Mathar_, Feb 25 2008: (Start) %C A091361 Proof of the conjecture that this is 1 and 2 followed by A016945 follows by considering the 6 cases n=6k-1, 6k, 6k+1, 6k+2, 6k+3 or 6k+4, individual evaluation of A001840(n) with their corresponding 3 formulas quoted in A001840 in each case and searching for solutions of the form A001840(n) = t*n for integer t. %C A091361 Example: A001840[6k+4]=A001840[3(2k+1)+1]=(2k+2)(6k+5)/2=t*(6k+4) implies t=k+7/6+1/[6(3k+2)] which cannot be solved in integers t and k. So numbers of the form 6k+4 are not members here. (End) %H A091361 M. Janjic and B. Petkovic, <a href="http://arxiv.org/abs/1301.4550">A Counting Function</a>, arXiv 1301.4550, 2013 %F A091361 G.f.: conjecture: 2*(1+x)/(1-x)/G(0) +x, where G(k)= 1 + 1/(1 - x*(3*k+1)/(x*(3*k+4) + 1/G(k+1))); (continued fraction). - _Sergei N. Gladkovskii_, Jun 06 2013 %e A091361 A001840(9)=18, so 9 is in the sequence. %t A091361 (* b = A001840 *) b[0] = 0; b[1] = 1; b[n_] := b[n] = n (n + 1)/2 - b[n - 1] - b[n - 2]; Reap[For[n = 1, n <= 400, n++, If[Mod[b[n], n] == 0, Sow[n]]]][[2, 1]] (* _Jean-François Alcover_, Feb 09 2019 *) %Y A091361 Cf. A001840. %K A091361 nonn %O A091361 1,2 %A A091361 _Jon Perry_, Mar 01 2004