cp's OEIS Frontend

A257006 Irregular triangle read by rows: period lengths of periods of primitive Zagier-reduced binary quadratic forms with discriminants D(n) = A079896(n).

%I A257006 #18 Jun 09 2025 00:53:53
%S A257006 1,2,2,1,3,5,4,3,1,4,2,5,2,5,4,1,6,4,7,6,4,11,6,3,5,1,6,2,10,7,8,2,9,
%T A257006 7,6,3,2,1,11,9,7,8,8,2,8,4,21,10,7,7,1,8,2,10,4,9,5,12,6
%N A257006 Irregular triangle read by rows: period lengths of periods of primitive Zagier-reduced binary quadratic forms with discriminants D(n) = A079896(n).
%C A257006 The possible positive nonsquare discriminants of binary quadratic forms are given in A079896.
%C A257006 For the definition of Zagier-reduced binary quadratic forms, see A257003.
%C A257006 A form is primitive if its coefficients are relatively prime.
%C A257006 The row sums give A257004(n), the number of primitive Zagier-reduced forms of discriminant D(n).
%C A257006 The number of entries in row n is A087048(n), the class number of primitive forms of discriminant D(n).
%D A257006 D. B. Zagier, Zetafunktionen und quadratische Körper, Springer, 1981.
%F A257006 a(n,k), n >= 1, k = 1, 2, ..., A079896(n), is the length of the k-th period of the primitive Zagier-reduced forms of discriminant D(n) = A079896(n). The lengths in row n are organized in nonincreasing order.
%e A257006 The table a(n,k) begins:
%e A257006 n/k  1   2   ...   D(n)    A087048(n)   A257004(n)
%e A257006 1:   1               5        1             1
%e A257006 2:   2               8        1             2
%e A257006 3:   2   1          12        2             3
%e A257006 4:   3              13        1             3
%e A257006 5:   5              17        1             5
%e A257006 6:   4              20        1             4
%e A257006 7:   3   1          21        2             4
%e A257006 8:   4   2          24        2             6
%e A257006 9:   5   2          28        2             7
%e A257006 10:  5              29        1             5
%e A257006 11:  4   1          32        2             5
%e A257006 12:  6   4          33        2            10
%e A257006 13:  7              37        1             7
%e A257006 14:  6   4          40        2            10
%e A257006 15: 11              41        1            11
%e A257006 16:  6   3          44        2             9
%e A257006 17:  5   1          45        2             6
%e A257006 18:  6   2          48        2             8
%e A257006 19: 10              52        1            10
%Y A257006 Cf. A257004, A257005, A079896, A225953, A079896.
%K A257006 nonn,tabf
%O A257006 1,2
%A A257006 _Barry R. Smith_, Apr 20 2015
%E A257006 Offset corrected by _Robin Visser_, Jun 08 2025