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Search: id:A002143
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| A002143 |
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Class numbers h(-p) where p runs though the primes p == 3 (mod 4).
(Formerly M2266 N0896)
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+0
6
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| 1, 1, 1, 1, 3, 3, 1, 5, 3, 1, 7, 5, 3, 5, 3, 5, 5, 3, 7, 1, 11, 5, 13, 9, 3, 7, 5, 15, 7, 13, 11, 3, 3, 19, 3, 5, 19, 9, 3, 17, 9, 21, 15, 5, 7, 7, 25, 7, 9, 3, 21, 5, 3, 9, 5, 7, 25, 13, 5, 13, 3, 23, 11, 5, 5, 31, 13, 5, 21, 15, 5, 7, 9, 7, 33, 7, 21, 3, 29, 3, 31, 19, 5, 11, 15, 27, 17, 13
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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a(n) = h(-A002145(n)).
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REFERENCES
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E. T. Ordman, Tables of the class number for negative prime discriminants, Math. Comp., 23 (1969), 458.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
Kevin A. Broughan, Restricted divisor sums, Acta Arithmetica, vol. 101, (2002), pp. 105-114.
N. Snyder, Lectures # 7: The Class Number Formula For Positive Definite Binary Quadratic Forms. [Background information on class numbers, link sent by V. S. Miller, Nov 22 2009]
Wikipedia, Class numbers of quadratic fields
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FORMULA
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h(-p) = 1 + 2*sum(0 <= n <= (1/2)*sqrt(p/3)-1, d(n^2+n+(p+1)/4, [2*n+1, sqrt(n^2+n+(p+1)/4)])) for prime p=3 mod 4, p>3. d(n, [a, b])=card{d: d|n and a<d<b} for integer n and real a, b. - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jul 19 2002
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EXAMPLE
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E.g. a(4) = 1 is the class number of -19, the 4-th prime == 3 mod 4
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CROSSREFS
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Cf. A002145 (primes p), A002146
Sequence in context: A111408 A092674 A111945 this_sequence A039739 A160496 A105663
Adjacent sequences: A002140 A002141 A002142 this_sequence A002144 A002145 A002146
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KEYWORD
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nonn,new
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jul 19 2002
Editorial comments from M. F. Hasler, Nov 22 2009
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