A191609 -id:A191609 - cp's OEIS frontend

A368424 Numbers k such that gcd(A019320(k), A019321(k)) > 1.

4, 11, 18, 20, 23, 28, 35, 43, 48, 52, 83, 95, 100, 119, 131, 138, 148, 155, 162, 166, 172, 179, 191, 196, 204, 210, 214, 239, 251, 253, 268, 292, 299, 300, 316, 323, 342, 359, 371, 378, 388, 419, 431, 443, 460, 463, 491, 500, 508, 515, 537, 556, 564, 575

Offset: 1

Tomohiro Yamada, Dec 24 2023

nonn

The corresponding greatest common divisors are given in A368425.

			a(1) = 4 since A019320(4) = 5 and A019321(4) = 10.

Robert Israel, Table of n, a(n) for n = 1..1000

Cf. A019320, A019321, A191609 (prime factors of such gcds), A368425.

select(k -> igcd(numtheory:-cyclotomic(k,2),
numtheory:-cyclotomic(k,3)) > 1, [$1..1000]); # Robert Israel, Dec 26 2023

Select[Range[600],GCD[Cyclotomic[#,2],Cyclotomic[#,3]]>1&] (* Stefano Spezia, Dec 26 2023 *)

for(n=1,1000,if(gcd(polcyclo(n,2),polcyclo(n,3))>1,print1(n,", ")))

A368425 The corresponding greatest common divisors to A368424(n).

Original entry on oeis.org

5, 23, 19, 5, 47, 29, 71, 431, 97, 53, 167, 191, 505, 239, 263, 139, 149, 311, 163, 499, 173, 359, 383, 197, 409, 211, 643, 479, 503, 23, 269, 293, 599, 1201, 317, 647, 19, 719, 743, 379, 389, 839, 863, 887, 461, 11113, 983, 5, 509, 1031, 4297, 557, 1129

Offset: 1

Tomohiro Yamada, Dec 24 2023

			a(2) = 23 since gcd(A019320(A368424(2)), A019321(A368424(2))) = gcd(2047, 88573) = 23.

Robert Israel, Table of n, a(n) for n = 1..1000

Cf. A019320, A019321, A191609 (primes dividing some term of this sequence), A368424.

subs(1=NULL, [seq(igcd(numtheory:-cyclotomic(n,2), numtheory:-cyclotomic(n,3)),n=1..1000)]); # Robert Israel, Dec 26 2023

Select[GCD[Cyclotomic[Range[600], 2], Cyclotomic[Range[600], 3]],#>1&] (* Stefano Spezia, Dec 26 2023 *)

for(n=1,1000,m=gcd(polcyclo(n,2),polcyclo(n,3));if(m>1,print1(m,", ")))

cp's OEIS Frontend

A368424 Numbers k such that gcd(A019320(k), A019321(k)) > 1.

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