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A257006 Irregular triangle read by rows: period lengths of periods of primitive Zagier-reduced binary quadratic forms with discriminants D(n) = A079896(n). 1
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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The possible positive nonsquare discriminants of binary quadratic forms are given in A079896.

For the definition of Zagier-reduced binary quadratic forms, see A257003.

A form is primitive if its coefficients are relatively prime.

The row sums give A257004(n), the number of primitive Zagier-reduced forms of discriminant D(n).

The number of entries in row n is A087048(n), the class number of primitive forms of discriminant D(n).

REFERENCES

D. B. Zagier, Zetafunktionen und quadratische K├Ârper, Springer, 1981.

LINKS

Table of n, a(n) for n=0..58.

FORMULA

a(n,k), n >= 0, 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.

EXAMPLE

The table a(n,k) begins:

n/k  1   2   ...   D(n)    A087048(n)   A257004(n)

0:   1               5        1             1

1:   2               8        1             2

2:   2   1          12        2             3

3:   3              13        1             3

4:   5              17        1             5

5:   4              20        1             4

6:   3   1          21        2             4

7:   4   2          24        2             6

8:   5   2          28        2             7

9:   5              29        1             5

10:  4   1          32        2             5

11:  6   4          33        2            10

12:  7              37        1             7

13:  6   4          40        2            10

14: 11              41        1            11

15:  6   3          44        2             9

16:  5   1          45        2             6

17:  6   2          48        2             8

18: 10              52        1            10

CROSSREFS

Cf. A257004, A257005, A079896, A225953, A079896.

Sequence in context: A228352 A303911 A205575 * A139687 A188181 A064581

Adjacent sequences:  A257003 A257004 A257005 * A257007 A257008 A257009

KEYWORD

nonn,tabf

AUTHOR

Barry R. Smith, Apr 20 2015

STATUS

approved

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Last modified July 12 09:35 EDT 2020. Contains 335657 sequences. (Running on oeis4.)