A103338 -id:A103338 - cp's OEIS frontend

A103335 Numbers whose smallest primitive root (A046145) is not prime.

1, 2, 41, 109, 151, 229, 251, 271, 313, 337, 362, 367, 409, 439, 542, 626, 674, 733, 761, 818, 878, 971, 991, 1021, 1031, 1069, 1289, 1297, 1303, 1429, 1471, 1489, 1681, 1759, 1783, 1789, 1811, 1871, 1873, 1879, 2062, 2137, 2342, 2411, 2441, 2551, 2594

Offset: 1

Harry J. Smith, Jan 31 2005

nonn

Robert Israel, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Primitive Root.

Cf. A001918, A046144, A046145, A046146, A103309, A103310, A103336, A103337, A103338.

filter:= proc(n)
  local r;
  r:= numtheory:-primroot(n);
  r <> FAIL and not isprime(r)
end proc:
filter(1):= true:
select(filter, [$1..3000]); Robert Israel, Sep 08 2020

L = {}; Do[ If[!PrimeQ[ Min[ Select[ Range[n], CoprimeQ[#, n] && MultiplicativeOrder[#, n] == CarmichaelLambda[n] &]]],
L = Append[L, n]], {n, 1, 3000}]; L (* Jonathan Sondow, May 17 2017 *)

Offset changed by Robert Israel, Sep 08 2020

A103336 Numbers whose largest primitive root (A046146) is not prime.

Original entry on oeis.org

1, 2, 11, 17, 19, 23, 29, 31, 37, 38, 41, 43, 47, 53, 58, 59, 62, 67, 71, 73, 74, 79, 81, 82, 83, 86, 89, 94, 97, 101, 107, 113, 118, 121, 122, 125, 127, 131, 134, 137, 139, 146, 149, 151, 157, 158, 162, 163, 167, 173, 178, 179, 191, 193, 194, 197, 211, 218, 223

Offset: 1

Harry J. Smith, Jan 31 2005

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Primitive Root.

Cf. A001918, A046144, A046145, A046146, A103309, A103310, A103335, A103337, A103338.

Select[Range[250], #==1 || ((p = PrimitiveRootList[#]) != {} && ! PrimeQ[Max @ p]) &] (* Amiram Eldar, Sep 25 2021 *)

Offset corrected by Amiram Eldar, Sep 25 2021

A103337 Smallest primitive root of numbers in sequence A103335.

Original entry on oeis.org

0, 1, 6, 6, 6, 6, 6, 6, 10, 10, 21, 6, 21, 15, 15, 15, 15, 6, 6, 21, 15, 6, 6, 10, 14, 6, 6, 10, 6, 6, 6, 14, 6, 6, 10, 6, 6, 14, 10, 6, 21, 10, 35, 6, 6, 6, 15, 6, 6, 10, 21, 14, 6, 33, 6, 6, 10, 6, 6, 6, 10, 6, 22, 15, 15, 6, 10, 12, 6, 15, 15, 10, 14, 21, 6, 15, 6, 6, 6, 6, 6, 6, 6, 10, 10, 6

Offset: 1

Harry J. Smith, Jan 31 2005

nonn

Robert Israel, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Primitive Root.

Cf. A001918, A046144, A046145, A046146, A103309, A103310, A103335, A103336, A103338.

# given list A103335 as at that sequence
[0,seq(numtheory:-primroot(A103335[i]),i=2..nops(A103335))]; # Robert Israel, Sep 08 2020

Offset changed by Robert Israel, Sep 08 2020

cp's OEIS Frontend

A103335 Numbers whose smallest primitive root (A046145) is not prime.

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A103336 Numbers whose largest primitive root (A046146) is not prime.

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A103337 Smallest primitive root of numbers in sequence A103335.

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