A191030 -id:A191030 - cp's OEIS frontend

A038919 Primes p such that 41 is a square mod p.

2, 5, 23, 31, 37, 41, 43, 59, 61, 73, 83, 103, 107, 113, 127, 131, 139, 163, 173, 197, 223, 241, 251, 269, 271, 277, 283, 307, 337, 349, 353, 359, 367, 373, 379, 389, 401, 409, 419, 431, 433, 443, 449, 461, 467

Offset: 1

N. J. A. Sloane

nonn

The only difference between this sequence and A191030 is the presence of a(6) = 41. - Zak Seidov, May 24 2013

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A191030. - Zak Seidov, May 24 2013

Select[Prime[Range[100]], JacobiSymbol[41, #] != -1 &] (* Vincenzo Librandi, Sep 07 2012 *)

A035223 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)p^(-s)+Kronecker(m,p)p^(-2s))^(-1) for m = 41.

Original entry on oeis.org

1, 2, 0, 3, 2, 0, 0, 4, 1, 4, 0, 0, 0, 0, 0, 5, 0, 2, 0, 6, 0, 0, 2, 0, 3, 0, 0, 0, 0, 0, 2, 6, 0, 0, 0, 3, 2, 0, 0, 8, 1, 0, 2, 0, 2, 4, 0, 0, 1, 6, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 4, 0, 7, 0, 0, 0, 0, 0, 0, 0, 4, 2, 4, 0, 0, 0, 0, 0, 10, 1

Offset: 1

N. J. A. Sloane

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

Cf. A038920, A191030.

a[n_] := DivisorSum[n, KroneckerSymbol[41, #] &]; Array[a, 100] (* Amiram Eldar, Nov 20 2023 *)

my(m = 41); direuler(p=2,101,1/(1-(kronecker(m,p)*(X-X^2))-X))

a(n) = sumdiv(n, d, kronecker(41, d)); \\ Amiram Eldar, Nov 20 2023

From Amiram Eldar, Nov 20 2023: (Start)
a(n) = Sum_{d|n} Kronecker(41, d).
Multiplicative with a(41^e) = 1, a(p^e) = (1+(-1)^e)/2 if Kronecker(41, p) = -1 (p is in A038920), and a(p^e) = e+1 if Kronecker(41, p) = 1 (p is in A191030).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2*log(5*sqrt(41)+32)/sqrt(41) = 1.299093061575... . (End)

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A038919 Primes p such that 41 is a square mod p.

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A035223 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)p^(-s)+Kronecker(m,p)p^(-2s))^(-1) for m = 41.

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cp's OEIS Frontend

A038919 Primes p such that 41 is a square mod p.

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Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A035223 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = 41.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

PARI

Formula

A035223 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)p^(-s)+Kronecker(m,p)p^(-2s))^(-1) for m = 41.