A105345 Primes p with class number h(-p) divisible by 16.

257, 353, 409, 521, 569, 809, 857, 953, 1129, 1153, 1201, 1217, 1249, 1657, 2113, 2137, 2153, 2273, 2377, 2521, 2617, 2633, 2657, 2729, 2833, 3209, 3217, 3761, 3769, 4481, 4993, 5569, 5801, 5897, 6217, 6329, 6449, 6529, 7177, 7193

Offset

1,1

Comments

These are a proper subset of the primes of the form x^2+32y^2 whose class numbers are divisible by 8.

References

Cohn, H. Introduction to the construction of class fields, Cambridge, 1985, pp. 147-151

Links

Table of n, a(n) for n=1..40.

Philip A. Leonard and Kenneth S. Williams, On the divisibility of the class numbers of Q(sqrt(-p)) and Q(sqrt(-2p)) by 16, Canadian Math Bulletin,v.25 (1982), pp. 200-6.

Example

h(-257)=16: binary quadratic forms of discriminant -4(257) are x^2+257y^2, 2x^2+2xy+129y^2, 3x^2+-2xy+86y^2, 6x^2+-2xy+43y^2,9x^2+-4xy+29y^2, 7x^2+-6xy+38y^2, 14x^2+-6xy+19y^2, 13x^2+-8xy+21y^2, 17x^2+-14xy+18y^2 for 16 forms (the +- forms count twice)

Crossrefs

Sequence in context: A289560 A256776 A252279 * A060261 A264348 A301619

Adjacent sequences: A105342 A105343 A105344 * A105346 A105347 A105348

Keyword

nonn

Author

John L. Drost, Apr 30 2005

Status

approved