A040069 -id:A040069 - cp's OEIS frontend

A040070 Primes p such that x^3 = 15 has no solution mod p.

13, 19, 37, 43, 61, 73, 97, 103, 109, 127, 139, 151, 157, 163, 181, 193, 199, 211, 241, 271, 307, 313, 337, 349, 373, 379, 409, 421, 433, 439, 457, 487, 499, 523, 547, 577, 601, 607, 613, 619, 631, 661, 691, 709

Offset: 1

N. J. A. Sloane

Complement of A040069 relative to A000040. - Vincenzo Librandi, Sep 17 2012

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

[p: p in PrimesUpTo(1000) | not exists{x : x in ResidueClassRing(p) | x^3 eq 15} ]; // Vincenzo Librandi, Sep 17 2012

ok[p_]:= Reduce[Mod[x^3 - 15, p] == 0, x, Integers] == False;Select[Prime[Range[200]], ok] (* Vincenzo Librandi, Sep 17 2012 *)

A058953 Numbers k of the form k=p*2^x, with p prime and x>=0, such that tau(k)-m = A058933(k) where tau(k) is the number of divisors of k and m is 0 or 1.

Original entry on oeis.org

2, 3, 10, 28, 176, 832, 4352, 19456, 47104, 1900544, 4063232, 77594624, 687865856, 2885681152

Offset: 1

Naohiro Nomoto, Jan 13 2001

(p=2 => m=1); ( Conjecture: [for p>2]; if p=A040069 then m=0 else m=1. )

Cf. A000005, A040069, A040070, A058933.

Offset corrected, title clarified, and a(12)-a(13) from Sean A. Irvine, Sep 07 2022

cp's OEIS Frontend

A040070 Primes p such that x^3 = 15 has no solution mod p.

Views

Author

Keywords

Comments

Links

Programs

Magma

Mathematica

A058953 Numbers k of the form k=p*2^x, with p prime and x>=0, such that tau(k)-m = A058933(k) where tau(k) is the number of divisors of k and m is 0 or 1.

Views

Author

Keywords

Comments

Crossrefs

Extensions