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A003643 Number of genera of Q(sqrt(-n)), n squarefree.
(Formerly M0194)
4
1, 1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 1, 4, 2, 1, 2, 2, 4, 1, 4, 2, 2, 2, 2, 2, 2, 4, 1, 2, 1, 2, 2, 2, 4, 2, 1, 2, 2, 4, 4, 1, 4, 4, 1, 2, 2, 4, 4, 1, 2, 1, 4, 2, 2, 2, 2, 4, 2, 2, 2, 2, 4, 1, 8, 2, 1, 2, 4, 2, 2, 4, 2, 2, 2, 2, 2, 1, 4, 4, 1, 4, 2, 2, 4, 1, 4, 2, 2, 4, 2, 2, 1, 4, 2, 2, 2, 2, 4, 1, 8, 2, 1, 4, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

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

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Index entries for sequences related to quadratic fields

FORMULA

a(n) = 2^(omega(A033197(n)) - 1). - Andrew Howroyd, Jul 24 2018

Let k = A005117(n) be the n-th squarefree number, then a(n) = 2^omega(k) if k == 1 (mod 4) and 2^(omega(k) - 1) otherwise. - Jianing Song, Jul 25 2018

MATHEMATICA

Function[If[Mod[#, 4] == 1, 2^PrimeOmega[#], 2^(PrimeOmega[#] - 1)]] /@ Select[Range[200], SquareFreeQ] (* Jean-Fran├žois Alcover, Sep 04 2019 *)

PROG

(PARI) for(n=1, 200, if(issquarefree(n), print1(2^(omega(n*if((-n)%4>1, 4, 1)) - 1), ", "))) \\ Andrew Howroyd, Jul 24 2018

CROSSREFS

Cf. A000924, A001221 (omega), A005117, A033197, A003640.

Sequence in context: A191971 A156051 A091267 * A092788 A058062 A102820

Adjacent sequences:  A003640 A003641 A003642 * A003644 A003645 A003646

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane, Mira Bernstein

STATUS

approved

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Last modified January 25 03:49 EST 2020. Contains 331241 sequences. (Running on oeis4.)