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 A273164 Irregular array read by rows: T(n, k) giving in row n the divisors of nonprime numbers that are 3 (mod 4). 1
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The length of row n is 2*A273165(n). 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. From Paul Curtz, Jul 31 2016: (Start) For each row n of length 2*r(n) one has: T(n, m)*T(n, 2*r(n)-m+1) = T(n, 2*r(n)),for m=1, 2, ... , r(n). From the second comment it follows that the row sums are congruent to 0 modulo 4. (End) LINKS FORMULA T(n, k) gives the k-th divisor of A091236(n) in increasing order. EXAMPLE The irregular array T(n, k) begins: n\k 1  2  3   4  5   6  7   8 ... 1:  1  3  5  15 2:  1  3  9  27 3:  1  5  7  35 4:  1  3 13  39 5:  1  3 17  51 6:  1  5 11  55 7:  1  3  7   9 21  63 8:  1  3  5  15 25  75 9:  1  3 29  87 10: 1  7 13  91 11: 1  5 19  95 12: 1  3  9  11 33  99 13: 1  3 37 111 14: 1  5 23 115 15: 1  7 17 119 16: 1  3 41 123 17: 1  3  5   9 15  27 45 135 18: 1 11 13 143 19: 1  3  7  21 49 147 20: 1 5 31 155 ... The irregular array modulo 4 gives (-1 for 3 (mod 4)): n\k 1  2  3   4  5   6  7   8 ... 1:  1  -1  1  -1 2:  1  -1  1  -1 3:  1   1 -1  -1 4:  1  -1  1  -1 5:  1  -1  1  -1 6:  1   1 -1  -1 7:  1  -1  1  -1  1  -1 8:  1  -1  1  -1  1  -1 9:  1  -1  1  -1 10: 1  -1  1  -1 11: 1   1 -1  -1 12: 1  -1  1  -1  1  -1 13: 1  -1  1  -1 14: 1   1 -1  -1 15: 1  -1  1  -1 16: 1  -1  1  -1 17: 1  -1  1   1  -1  -1  1 -1 18: 1  -1  1  -1 19: 1  -1 -1   1   1  -1 20: 1   1 -1  -1 ... MATHEMATICA Divisors@ Select[Range@ 155, CompositeQ@ # && Mod[#, 4] == 3 &] // Flatten (* Michael De Vlieger, Aug 01 2016 *) CROSSREFS Cf. A004767, A078703, A091236, A273165. Sequence in context: A129326 A167553 A118562 * A317661 A115043 A272255 Adjacent sequences:  A273161 A273162 A273163 * A273165 A273166 A273167 KEYWORD nonn,easy,tabf AUTHOR Wolfdieter Lang, Jul 29 2016 STATUS approved

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Last modified August 12 16:40 EDT 2020. Contains 336439 sequences. (Running on oeis4.)