cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A297175 Rational primes that decompose in the field Q(sqrt(19)).

Original entry on oeis.org

3, 5, 17, 31, 59, 61, 67, 71, 73, 79, 101, 103, 107, 127, 137, 149, 151, 157, 167, 179, 197, 211, 223, 227, 229, 233, 277, 307, 313, 331, 349, 353, 379, 383, 389, 397, 431, 439, 457, 461, 487, 523, 541, 547, 557, 563, 577, 593, 599, 607, 613, 617, 653
Offset: 1

Views

Author

N. J. A. Sloane, Dec 26 2017

Keywords

Links

Crossrefs

Cf. A297176, A038891, A038892.

Programs

A297176 Inert rational primes in the field Q(sqrt(19)).

Original entry on oeis.org

7, 11, 13, 23, 29, 37, 41, 43, 47, 53, 83, 89, 97, 109, 113, 131, 139, 163, 173, 181, 191, 193, 199, 239, 241, 251, 257, 263, 269, 271, 281, 283, 293, 311, 317, 337, 347, 359, 367, 373, 401, 409, 419, 421, 433, 443, 449, 463, 467, 479, 491, 499, 503, 509, 521, 569
Offset: 1

Views

Author

N. J. A. Sloane, Dec 26 2017

Keywords

Links

Crossrefs

Cf. A038892.

Programs

A035201 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = 19.

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A038892, A297175.

Programs

  • Mathematica
    a[n_] := DivisorSum[n, KroneckerSymbol[19, #] &]; Array[a, 100] (* Amiram Eldar, Nov 19 2023 *)
  • PARI
    my(m = 19); direuler(p=2,101,1/(1-(kronecker(m,p)*(X-X^2))-X))
  • PARI
    a(n) = sumdiv(n, d, kronecker(19, d)); \\ Amiram Eldar, Nov 19 2023

Formula

From Amiram Eldar, Nov 19 2023: (Start)
a(n) = Sum_{d|n} Kronecker(19, d).
Multiplicative with a(19^e) = 1, a(p^e) = (1+(-1)^e)/2 if Kronecker(19, p) = -1 (p is in A038892), and a(p^e) = e+1 if Kronecker(19, p) = 1 (p is in A297175).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2*log(39*sqrt(19)+170)/(3*sqrt(19)) = 0.891499901309... . (End)
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.