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A003642 Number of genera of imaginary quadratic field with discriminant -k, k = A191483(n).
(Formerly M0211)
3
1, 1, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 4, 4, 2, 2, 2, 2, 4, 2, 2, 4, 2, 2, 2, 4, 4, 4, 4, 2, 2, 4, 4, 2, 4, 2, 2, 4, 2, 2, 2, 4, 8, 2, 2, 4, 2, 4, 2, 2, 4, 4, 4, 2, 2, 4, 4, 2, 4, 2, 2, 4, 2, 2, 4, 8, 2, 4, 2, 4, 4, 2, 2, 4, 4, 4, 4, 2, 2, 2, 4, 2, 4, 2, 4, 8, 4, 2, 4, 2, 4, 4, 2, 2, 4, 2, 4, 4, 2, 4, 4, 4, 2, 2, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

REFERENCES

D. A. Buell, Binary Quadratic Forms. Springer-Verlag, NY, 1989, pp. 224-241.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=1..105.

Index entries for sequences related to quadratic fields

FORMULA

a(n) = 2^(omega(A191483(n)) - 1). - Jianing Song, Jul 24 2018

MATHEMATICA

2^(PrimeNu[Select[Range[1000], Mod[#, 4] == 0 && SquareFreeQ[#/4] && Mod[#, 16] != 12&]] - 1) (* Jean-Fran├žois Alcover, Jul 25 2019, after Andrew Howroyd in A191483 *)

PROG

(PARI) for(n=1, 1000, if(isfundamental(-n) && n%2==0, print1(2^(omega(n) - 1), ", "))) \\ Andrew Howroyd, Jul 24 2018

CROSSREFS

Cf. A001221 (omega), A003640, A003641, A191483.

Sequence in context: A307833 A083261 A003648 * A100007 A104369 A051702

Adjacent sequences:  A003639 A003640 A003641 * A003643 A003644 A003645

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Mira Bernstein

EXTENSIONS

Name clarified by Jianing Song, Jul 24 2018

STATUS

approved

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Last modified December 8 14:38 EST 2019. Contains 329865 sequences. (Running on oeis4.)