A035175 -id:A035175 - cp's OEIS frontend

A035188 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)p^(-s)+Kronecker(m,p)p^(-2s))^(-1) for m = 6.

1, 1, 1, 1, 2, 1, 0, 1, 1, 2, 0, 1, 0, 0, 2, 1, 0, 1, 2, 2, 0, 0, 2, 1, 3, 0, 1, 0, 2, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 1, 1, 3, 0, 0, 2, 1, 0, 0, 2, 2, 0, 2, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 2, 1, 2, 0, 3, 2, 0, 0, 0, 2, 1

Offset: 1

N. J. A. Sloane

Coefficients of Dedekind zeta function for the quadratic number field of discriminant 24. See A002324 for formula and Maple code. - N. J. A. Sloane, Mar 22 2022

G. C. Greubel, Table of n, a(n) for n = 1..10000

Dedekind zeta functions for imaginary quadratic number fields of discriminants -3, -4, -7, -8, -11, -15, -19, -20 are A002324, A002654, A035182, A002325, A035179, A035175, A035171, A035170, respectively.
Dedekind zeta functions for real quadratic number fields of discriminants 5, 8, 12, 13, 17, 21, 24, 28, 29, 33, 37, 40 are A035187, A035185, A035194, A035195, A035199, A035203, A035188, A035210, A035211, A035215, A035219, A035192, respectively.
Cf. A038877, A097934.

a[n_] := If[n < 0, 0, DivisorSum[n, KroneckerSymbol[6, #] &]]; Table[ a[n], {n, 1, 100}] (* G. C. Greubel, Apr 27 2018 *)

my(m=6); direuler(p=2,101,1/(1-(kronecker(m,p)*(X-X^2))-X))

a(n) = sumdiv(n, d, kronecker(6, d)); \\ Amiram Eldar, Nov 20 2023

From Amiram Eldar, Oct 17 2022: (Start)
a(n) = Sum_{d|n} Kronecker(6, d).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = log(5+2*sqrt(6)) / sqrt(6) = 0.935881... . (End)
Multiplicative with a(p^e) = 1 if Kronecker(6, p) = 0 (p = 2 or 3), a(p^e) = (1+(-1)^e)/2 if Kronecker(6, p) = -1 (p is in A038877), and a(p^e) = e+1 if Kronecker(6, p) = 1 (p is in A097934). - Amiram Eldar, Nov 20 2023

A035195 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)p^(-s)+Kronecker(m,p)p^(-2s))^(-1) for m = 13.

Original entry on oeis.org

1, 0, 2, 1, 0, 0, 0, 0, 3, 0, 0, 2, 1, 0, 0, 1, 2, 0, 0, 0, 0, 0, 2, 0, 1, 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, 3, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 1, 0, 4, 1, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 5

Offset: 1

N. J. A. Sloane

Coefficients of Dedekind zeta function for the quadratic number field of discriminant 13. See A002324 for formula and Maple code. - N. J. A. Sloane, Mar 22 2022

G. C. Greubel, Table of n, a(n) for n = 1..10000

Dedekind zeta functions for imaginary quadratic number fields of discriminants -3, -4, -7, -8, -11, -15, -19, -20 are A002324, A002654, A035182, A002325, A035179, A035175, A035171, A035170, respectively.
Dedekind zeta functions for real quadratic number fields of discriminants 5, 8, 12, 13, 17, 21, 24, 28, 29, 33, 37, 40 are A035187, A035185, A035194, A035195, A035199, A035203, A035188, A035210, A035211, A035215, A035219, A035192, respectively.
Cf. A038883, A038884.

a[n_] := If[n < 0, 0, DivisorSum[n, KroneckerSymbol[13, #] &]]; Table[ a[n], {n, 1, 100}] (* G. C. Greubel, Apr 27 2018 *)

my(m=13); direuler(p=2,101,1/(1-(kronecker(m,p)*(X-X^2))-X))

a(n) = sumdiv(n, d, kronecker(13, d)); \\ Amiram Eldar, Nov 18 2023

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2*log((3+sqrt(13))/2)/sqrt(13) = 0.662735... . - Amiram Eldar, Oct 11 2022
From Amiram Eldar, Nov 18 2023: (Start)
a(n) = Sum_{d|n} Kronecker(13, d).
Multiplicative with a(13^e) = 1, a(p^e) = (1+(-1)^e)/2 if Kronecker(13, p) = -1 (p is in A038884), and a(p^e) = e+1 if Kronecker(13, p) = 1 (p is in A038883 \ {13}). (End)

A035199 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)p^(-s)+Kronecker(m,p)p^(-2s))^(-1) for m = 17.

Original entry on oeis.org

1, 2, 0, 3, 0, 0, 0, 4, 1, 0, 0, 0, 2, 0, 0, 5, 1, 2, 2, 0, 0, 0, 0, 0, 1, 4, 0, 0, 0, 0, 0, 6, 0, 2, 0, 3, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 1, 2, 0, 6, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 7, 0, 0, 2, 3, 0, 0, 0, 4, 0, 0, 0, 6, 0, 0, 0, 0, 1

Offset: 1

N. J. A. Sloane

Coefficients of Dedekind zeta function for the quadratic number field of discriminant 17. See A002324 for formula and Maple code. - N. J. A. Sloane, Mar 22 2022

G. C. Greubel, Table of n, a(n) for n = 1..10000

Dedekind zeta functions for imaginary quadratic number fields of discriminants -3, -4, -7, -8, -11, -15, -19, -20 are A002324, A002654, A035182, A002325, A035179, A035175, A035171, A035170, respectively.
Dedekind zeta functions for real quadratic number fields of discriminants 5, 8, 12, 13, 17, 21, 24, 28, 29, 33, 37, 40 are A035187, A035185, A035194, A035195, A035199, A035203, A035188, A035210, A035211, A035215, A035219, A035192, respectively.
Cf. A038889, A038890.

a[n_] := If[n < 0, 0, DivisorSum[n, KroneckerSymbol[17, #] &]]; Table[ a[n], {n, 1, 100}] (* G. C. Greubel, Apr 27 2018 *)

my(m=17); direuler(p=2,101,1/(1-(kronecker(m,p)*(X-X^2))-X))

a(n) = sumdiv(n, d, kronecker(17, d)); \\ Amiram Eldar, Nov 18 2023

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2*log(4+sqrt(17))/sqrt(17) = 1.016084... . - Amiram Eldar, Oct 11 2022
From Amiram Eldar, Nov 18 2023: (Start)
a(n) = Sum_{d|n} Kronecker(17, d).
Multiplicative with a(17^e) = 1, a(p^e) = (1+(-1)^e)/2 if Kronecker(17, p) = -1 (p is in A038890), and a(p^e) = e+1 if Kronecker(17, p) = 1 (p is in A038889 \ {17}). (End)

A035192 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)p^(-s)+Kronecker(m,p)p^(-2s))^(-1) for m = 10.

Original entry on oeis.org

1, 1, 2, 1, 1, 2, 0, 1, 3, 1, 0, 2, 2, 0, 2, 1, 0, 3, 0, 1, 0, 0, 0, 2, 1, 2, 4, 0, 0, 2, 2, 1, 0, 0, 0, 3, 2, 0, 4, 1, 2, 0, 2, 0, 3, 0, 0, 2, 1, 1, 0, 2, 2, 4, 0, 0, 0, 0, 0, 2, 0, 2, 0, 1, 2, 0, 2, 0, 0, 0, 2, 3, 0, 2, 2, 0, 0, 4, 2, 1, 5

Offset: 1

N. J. A. Sloane

Coefficients of Dedekind zeta function for the quadratic number field of discriminant 40. See A002324 for formula and Maple code. - N. J. A. Sloane, Mar 22 2022

G. C. Greubel, Table of n, a(n) for n = 1..10000

Dedekind zeta functions for imaginary quadratic number fields of discriminants -3, -4, -7, -8, -11, -15, -19, -20 are A002324, A002654, A035182, A002325, A035179, A035175, A035171, A035170, respectively.
Dedekind zeta functions for real quadratic number fields of discriminants 5, 8, 12, 13, 17, 21, 24, 28, 29, 33, 37, 40 are A035187, A035185, A035194, A035195, A035199, A035203, A035188, A035210, A035211, A035215, A035219, A035192, respectively.
Cf. A038880, A097955.

a[n_] := If[n < 0, 0, DivisorSum[n, KroneckerSymbol[10, #] &]]; Table[ a[n], {n, 1, 100}] (* G. C. Greubel, Apr 27 2018 *)

my(m=10); direuler(p=2,101,1/(1-(kronecker(m,p)*(X-X^2))-X))

a(n) = sumdiv(n, d, kronecker(10, d)); \\ Amiram Eldar, Nov 18 2023

From Amiram Eldar, Nov 18 2023: (Start)
a(n) = Sum_{d|n} Kronecker(10, d).
Multiplicative with a(p^e) = 1 if Kronecker(10, p) = 0 (p = 2 or 5), a(p^e) = (1+(-1)^e)/2 if Kronecker(10, p) = -1 (p is in A038880), and a(p^e) = e+1 if Kronecker(10, p) = 1 (p is in A097955).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2*log(sqrt(10)+3)/sqrt(10) = 1.1500865228... . (End)

A035194 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)p^(-s)+Kronecker(m,p)p^(-2s))^(-1) for m = 12.

Original entry on oeis.org

1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 2, 1, 2, 0, 0, 1, 0, 1, 0, 0, 0, 2, 2, 1, 1, 2, 1, 0, 0, 0, 0, 1, 2, 0, 0, 1, 2, 0, 2, 0, 0, 0, 0, 2, 0, 2, 2, 1, 1, 1, 0, 2, 0, 1, 0, 0, 0, 0, 2, 0, 2, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 1, 2, 2, 1, 0, 0, 2, 0, 0, 1

Offset: 1

N. J. A. Sloane

Coefficients of Dedekind zeta function for the quadratic number field of discriminant 12. See A002324 for formula and Maple code. - N. J. A. Sloane, Mar 22 2022

G. C. Greubel, Table of n, a(n) for n = 1..10000

Dedekind zeta functions for imaginary quadratic number fields of discriminants -3, -4, -7, -8, -11, -15, -19, -20 are A002324, A002654, A035182, A002325, A035179, A035175, A035171, A035170, respectively.
Dedekind zeta functions for real quadratic number fields of discriminants 5, 8, 12, 13, 17, 21, 24, 28, 29, 33, 37, 40 are A035187, A035185, A035194, A035195, A035199, A035203, A035188, A035210, A035211, A035215, A035219, A035192, respectively.
Cf. A003630, A097933, A196530.

a[n_] := If[n < 0, 0, DivisorSum[n, KroneckerSymbol[12, #] &]]; Table[ a[n], {n, 1, 100}] (* G. C. Greubel, Apr 27 2018 *)

my(m=12); direuler(p=2,101,1/(1-(kronecker(m,p)*(X-X^2))-X))

a(n) = sumdiv(n, d, kronecker(12, d)); \\ Amiram Eldar, Nov 18 2023

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = log(2+sqrt(3))/sqrt(3) = 0.760345... (A196530). - Amiram Eldar, Oct 11 2022
From Amiram Eldar, Nov 18 2023: (Start)
a(n) = Sum_{d|n} Kronecker(12, d).
Multiplicative with a(p^e) = 1 if Kronecker(12, p) = 0 (p = 2 or 3), a(p^e) = (1+(-1)^e)/2 if Kronecker(12, p) = -1 (p is in A003630), and a(p^e) = e+1 if Kronecker(12, p) = 1 (p is in A097933). (End)

A035210 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)p^(-s)+Kronecker(m,p)p^(-2s))^(-1) for m = 28.

Original entry on oeis.org

1, 1, 2, 1, 0, 2, 1, 1, 3, 0, 0, 2, 0, 1, 0, 1, 0, 3, 2, 0, 2, 0, 0, 2, 1, 0, 4, 1, 2, 0, 2, 1, 0, 0, 0, 3, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 1, 1, 0, 0, 2, 4, 0, 1, 4, 2, 2, 0, 0, 2, 3, 1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 2, 2, 2, 0, 0, 0, 0, 5

Offset: 1

N. J. A. Sloane

Coefficients of Dedekind zeta function for the quadratic number field of discriminant 28. See A002324 for formula and Maple code. - N. J. A. Sloane, Mar 22 2022

Amiram Eldar, Table of n, a(n) for n = 1..10000

Dedekind zeta functions for imaginary quadratic number fields of discriminants -3, -4, -7, -8, -11, -15, -19, -20 are A002324, A002654, A035182, A002325, A035179, A035175, A035171, A035170, respectively.
Dedekind zeta functions for real quadratic number fields of discriminants 5, 8, 12, 13, 17, 21, 24, 28, 29, 33, 37, 40 are A035187, A035185, A035194, A035195, A035199, A035203, A035188, A035210, A035211, A035215, A035219, A035192, respectively.
Cf. A003632, A296934.

a[n_] := DivisorSum[n, KroneckerSymbol[28, #] &]; Array[a, 100] (* Amiram Eldar, Nov 19 2023 *)

my(m = 28); direuler(p=2,101,1/(1-(kronecker(m,p)*(X-X^2))-X))

a(n) = sumdiv(n, d, kronecker(28, d)); \\ Amiram Eldar, Nov 19 2023

From Amiram Eldar, Nov 19 2023: (Start)
a(n) = Sum_{d|n} Kronecker(28, d).
Multiplicative with a(p^e) = 1 if Kronecker(28, p) = 0 (p = 2 or 7), a(p^e) = (1+(-1)^e)/2 if Kronecker(28, p) = -1 (p is in A003632), and a(p^e) = e+1 if Kronecker(28, p) = 1 (p is in A296934).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = log(3*sqrt(7)+8)/sqrt(7) = 1.046454884756... . (End)

A035211 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)p^(-s)+Kronecker(m,p)p^(-2s))^(-1) for m = 29.

Original entry on oeis.org

1, 0, 0, 1, 2, 0, 2, 0, 1, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 0, 3, 0, 0, 2, 1, 0, 0, 0, 0, 0, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 1, 4, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1

Offset: 1

N. J. A. Sloane

Coefficients of Dedekind zeta function for the quadratic number field of discriminant 29. See A002324 for formula and Maple code. - N. J. A. Sloane, Mar 22 2022

Amiram Eldar, Table of n, a(n) for n = 1..10000

Dedekind zeta functions for imaginary quadratic number fields of discriminants -3, -4, -7, -8, -11, -15, -19, -20 are A002324, A002654, A035182, A002325, A035179, A035175, A035171, A035170, respectively.
Dedekind zeta functions for real quadratic number fields of discriminants 5, 8, 12, 13, 17, 21, 24, 28, 29, 33, 37, 40 are A035187, A035185, A035194, A035195, A035199, A035203, A035188, A035210, A035211, A035215, A035219, A035192, respectively.
Cf. A038902, A191022.

a[n_] := DivisorSum[n, KroneckerSymbol[29, #] &]; Array[a, 100] (* Amiram Eldar, Nov 19 2023 *)

my(m = 29); direuler(p=2,101,1/(1-(kronecker(m,p)*(X-X^2))-X))

a(n) = sumdiv(n, d, kronecker(29, d)); \\ Amiram Eldar, Nov 19 2023

From Amiram Eldar, Nov 19 2023: (Start)
a(n) = Sum_{d|n} Kronecker(29, d).
Multiplicative with a(29^e) = 1, a(p^e) = (1+(-1)^e)/2 if Kronecker(29, p) = -1 (p is in A038902), and a(p^e) = e+1 if Kronecker(29, p) = 1 (p is in A191022).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2*log((sqrt(29)+5)/2)/sqrt(29) = 0.611766289562... . (End)

A035219 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)p^(-s)+Kronecker(m,p)p^(-2s))^(-1) for m = 37.

Original entry on oeis.org

1, 0, 2, 1, 0, 0, 2, 0, 3, 0, 2, 2, 0, 0, 0, 1, 0, 0, 0, 0, 4, 0, 0, 0, 1, 0, 4, 2, 0, 0, 0, 0, 4, 0, 0, 3, 1, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 3, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 1, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 0, 4, 0, 0, 0, 5

Offset: 1

N. J. A. Sloane

Coefficients of Dedekind zeta function for the quadratic number field of discriminant 37. See A002324 for formula and Maple code. - N. J. A. Sloane, Mar 22 2022

Amiram Eldar, Table of n, a(n) for n = 1..10000

Dedekind zeta functions for imaginary quadratic number fields of discriminants -3, -4, -7, -8, -11, -15, -19, -20 are A002324, A002654, A035182, A002325, A035179, A035175, A035171, A035170, respectively.
Dedekind zeta functions for real quadratic number fields of discriminants 5, 8, 12, 13, 17, 21, 24, 28, 29, 33, 37, 40 are A035187, A035185, A035194, A035195, A035199, A035203, A035188, A035210, A035211, A035215, A035219, A035192, respectively.
Cf. A038914, A191027.

a[n_] := DivisorSum[n, KroneckerSymbol[37, #] &]; Array[a, 100] (* Amiram Eldar, Nov 20 2023 *)

my(m = 37); direuler(p=2,101,1/(1-(kronecker(m,p)*(X-X^2))-X))

a(n) = sumdiv(n, d, kronecker(37, d)); \\ Amiram Eldar, Nov 20 2023

From Amiram Eldar, Nov 20 2023: (Start)
a(n) = Sum_{d|n} Kronecker(37, d).
Multiplicative with a(37^e) = 1, a(p^e) = (1+(-1)^e)/2 if Kronecker(37, p) = -1 (p is in A038914), and a(p^e) = e+1 if Kronecker(37, p) = 1 (p is in A191027).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2*log(sqrt(37)+6)/sqrt(37) = 0.819292168725... . (End)

A035215 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)p^(-s)+Kronecker(m,p)p^(-2s))^(-1) for m = 33.

Original entry on oeis.org

1, 2, 1, 3, 0, 2, 0, 4, 1, 0, 1, 3, 0, 0, 0, 5, 2, 2, 0, 0, 0, 2, 0, 4, 1, 0, 1, 0, 2, 0, 2, 6, 1, 4, 0, 3, 2, 0, 0, 0, 2, 0, 0, 3, 0, 0, 0, 5, 1, 2, 2, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 4, 0, 7, 0, 2, 2, 6, 0, 0, 0, 4, 0, 4, 1, 0, 0, 0, 0, 0, 1

Offset: 1

N. J. A. Sloane

Coefficients of Dedekind zeta function for the quadratic number field of discriminant 33. See A002324 for formula and Maple code. - N. J. A. Sloane, Mar 22 2022

Amiram Eldar, Table of n, a(n) for n = 1..10000

Dedekind zeta functions for imaginary quadratic number fields of discriminants -3, -4, -7, -8, -11, -15, -19, -20 are A002324, A002654, A035182, A002325, A035179, A035175, A035171, A035170, respectively.
Dedekind zeta functions for real quadratic number fields of discriminants 5, 8, 12, 13, 17, 21, 24, 28, 29, 33, 37, 40 are A035187, A035185, A035194, A035195, A035199, A035203, A035188, A035210, A035211, A035215, A035219, A035192, respectively.
Cf. A038907, A038908.

a[n_] := DivisorSum[n, KroneckerSymbol[33, #] &]; Array[a, 100] (* Amiram Eldar, Nov 19 2023 *)

my(m = 33); direuler(p=2,101,1/(1-(kronecker(m,p)*(X-X^2))-X))

a(n) = sumdiv(n, d, kronecker(33, d)); \\ Amiram Eldar, Nov 19 2023

From Amiram Eldar, Nov 19 2023: (Start)
a(n) = Sum_{d|n} Kronecker(33, d).
Multiplicative with a(p^e) = 1 if Kronecker(33, p) = 0 (p = 3 or 11), a(p^e) = (1+(-1)^e)/2 if Kronecker(33, p) = -1 (p is in A038908), and a(p^e) = e+1 if Kronecker(33, p) = 1 (p is in A038907 \ {3, 11}).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2*log(4*sqrt(33)+23)/sqrt(33) = 1.332797188186... . (End)

A341786 Norms of prime ideals in Z[(1+sqrt(-15))/2], the ring of integers of Q(sqrt(-15)).

Original entry on oeis.org

2, 3, 5, 17, 19, 23, 31, 47, 49, 53, 61, 79, 83, 107, 109, 113, 121, 137, 139, 151, 167, 169, 173, 181, 197, 199, 211, 227, 229, 233, 241, 257, 263, 271, 293, 317, 331, 347, 349, 353, 379, 383, 409, 421, 439, 443, 467, 499, 503, 541, 557, 563, 571, 587

Offset: 1

Jianing Song, Feb 19 2021

The norm of a nonzero ideal I in a ring R is defined as the size of the quotient ring R/I.
Note that Z[(1+sqrt(-15))/2] has class number 2.
Consists of the primes congruent to 1, 2, 3, 4, 5, 8 modulo 15 and the squares of primes congruent to 7, 11, 13, 14 modulo 15.
For primes p == 1, 4 (mod 15), there are two distinct ideals with norm p in Z[(1+sqrt(-15))/2], namely (x + y*(1+sqrt(-15))/2) and (x + y*(1-sqrt(-15))/2), where (x,y) is a solution to x^2 + x*y + 4*y^2 = p; for p == 2, 8 (mod 15), there are also two distinct ideals with norm p, namely (p, x + y*(1+sqrt(-15))/2) and (p, x + y*(1-sqrt(-15))/2), where (x,y) is a solution to x^2 + x*y + 4*y^2 = p^2 with y != 0; (3, sqrt(-15)) and (5, sqrt(-15)) are respectively the unique ideal with norm 3 and 5; for p == 7, 11, 13, 14 (mod 15), (p) is the only ideal with norm p^2.

			Let |I| be the norm of an ideal I, then:
|(2, (1+sqrt(-15))/2)| = |(2, (1-sqrt(-15))/2)| = 2;
|(3, sqrt(-15))| = 3;
|(5, sqrt(-15))| = 5;
|(17, 7+4*sqrt(-15))| = |(17, 7-4*sqrt(-15))| = 17;
|(2 + sqrt(-15))| = |(2 - sqrt(-15))| = 19;
|(23, 17+4*sqrt(-15))| = |(23, 17-4*sqrt(-15))| = 23;
|(4 + sqrt(-15))| = |(4 - sqrt(-15))| = 31.

Jianing Song, Table of n, a(n) for n = 1..10000

Cf. A316569, A033212, A106859, A191018, A191062.
The number of distinct ideals with norm n is given by A035175.
Norms of prime ideals in O_K, where K is the quadratic field with discriminant D and O_K be the ring of integers of K: A055673 (D=8), A341783 (D=5), A055664 (D=-3), A055025 (D=-4), A090348 (D=-7), A341784 (D=-8), A341785 (D=-11), this sequence (D=-15*), A341787 (D=-19), A091727 (D=-20*), A341788 (D=-43), A341789 (D=-67), A341790 (D=-163). Here a "*" indicates the cases where O_K is not a unique factorization domain.

isA341786(n) = my(disc=-15); (isprime(n) && kronecker(disc,n)>=0) || (issquare(n, &n) && isprime(n) && kronecker(disc,n)==-1)

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A035188 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = 6.

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A035195 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = 13.

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A035199 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = 17.

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A035192 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = 10.

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A035194 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = 12.

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A035210 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = 28.

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A035211 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = 29.

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A035188 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)p^(-s)+Kronecker(m,p)p^(-2s))^(-1) for m = 6.

A035195 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)p^(-s)+Kronecker(m,p)p^(-2s))^(-1) for m = 13.

A035199 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)p^(-s)+Kronecker(m,p)p^(-2s))^(-1) for m = 17.

A035192 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)p^(-s)+Kronecker(m,p)p^(-2s))^(-1) for m = 10.

A035194 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)p^(-s)+Kronecker(m,p)p^(-2s))^(-1) for m = 12.

A035210 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)p^(-s)+Kronecker(m,p)p^(-2s))^(-1) for m = 28.

A035211 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)p^(-s)+Kronecker(m,p)p^(-2s))^(-1) for m = 29.

A035219 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)p^(-s)+Kronecker(m,p)p^(-2s))^(-1) for m = 37.

A035215 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)p^(-s)+Kronecker(m,p)p^(-2s))^(-1) for m = 33.