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 A273164 #25 Aug 03 2016 09:01:49 %S A273164 1,3,5,15,1,3,9,27,1,5,7,35,1,3,13,39,1,3,17,51,1,5,11,55,1,3,7,9,21, %T A273164 63,1,3,5,15,25,75,1,3,29,87,1,7,13,91,1,5,19,95,1,3,9,11,33,99,1,3, %U A273164 37,111,1,5,23,115,1,7,17,119,1,3,41,123,1,3,5,9,15,27,45,135,1,11,13,143,1,3,7,21,49,147,1,5,31,155 %N A273164 Irregular array read by rows: T(n, k) giving in row n the divisors of nonprime numbers that are 3 (mod 4). %C A273164 The length of row n is 2*A273165(n). %C A273164 The number of divisors 1 and -1 (mod 4) in each row are identical, namely A273165(n). See the Jan 05 2004 Jovovic comment on A078703. For prime numbers 3 (mod 4) this is obvious. For the proof see a comment on A091236 with the Grosswald reference. %C A273164 From _Paul Curtz_, Jul 31 2016: (Start) %C A273164 For each row n of length 2*r(n) one has: %C A273164 T(n, m)*T(n, 2*r(n)-m+1) = T(n, 2*r(n)),for m=1, 2, ... , r(n). %C A273164 From the second comment it follows that the row sums are congruent to 0 modulo 4. (End) %F A273164 T(n, k) gives the k-th divisor of A091236(n) in increasing order. %e A273164 The irregular array T(n, k) begins: %e A273164 n\k 1 2 3 4 5 6 7 8 ... %e A273164 1: 1 3 5 15 %e A273164 2: 1 3 9 27 %e A273164 3: 1 5 7 35 %e A273164 4: 1 3 13 39 %e A273164 5: 1 3 17 51 %e A273164 6: 1 5 11 55 %e A273164 7: 1 3 7 9 21 63 %e A273164 8: 1 3 5 15 25 75 %e A273164 9: 1 3 29 87 %e A273164 10: 1 7 13 91 %e A273164 11: 1 5 19 95 %e A273164 12: 1 3 9 11 33 99 %e A273164 13: 1 3 37 111 %e A273164 14: 1 5 23 115 %e A273164 15: 1 7 17 119 %e A273164 16: 1 3 41 123 %e A273164 17: 1 3 5 9 15 27 45 135 %e A273164 18: 1 11 13 143 %e A273164 19: 1 3 7 21 49 147 %e A273164 20: 1 5 31 155 %e A273164 ... %e A273164 The irregular array modulo 4 gives (-1 for 3 (mod 4)): %e A273164 n\k 1 2 3 4 5 6 7 8 ... %e A273164 1: 1 -1 1 -1 %e A273164 2: 1 -1 1 -1 %e A273164 3: 1 1 -1 -1 %e A273164 4: 1 -1 1 -1 %e A273164 5: 1 -1 1 -1 %e A273164 6: 1 1 -1 -1 %e A273164 7: 1 -1 1 -1 1 -1 %e A273164 8: 1 -1 1 -1 1 -1 %e A273164 9: 1 -1 1 -1 %e A273164 10: 1 -1 1 -1 %e A273164 11: 1 1 -1 -1 %e A273164 12: 1 -1 1 -1 1 -1 %e A273164 13: 1 -1 1 -1 %e A273164 14: 1 1 -1 -1 %e A273164 15: 1 -1 1 -1 %e A273164 16: 1 -1 1 -1 %e A273164 17: 1 -1 1 1 -1 -1 1 -1 %e A273164 18: 1 -1 1 -1 %e A273164 19: 1 -1 -1 1 1 -1 %e A273164 20: 1 1 -1 -1 %e A273164 ... %t A273164 Divisors@ Select[Range@ 155, CompositeQ@ # && Mod[#, 4] == 3 &] // Flatten (* _Michael De Vlieger_, Aug 01 2016 *) %Y A273164 Cf. A004767, A078703, A091236, A273165. %K A273164 nonn,easy,tabf %O A273164 1,2 %A A273164 _Wolfdieter Lang_, Jul 29 2016