A324583 Numbers k such that k and A276086(k) are coprime, where A276086 is the primorial base exp-function.

0, 1, 2, 4, 5, 6, 7, 8, 11, 12, 13, 14, 16, 17, 18, 19, 22, 23, 24, 26, 28, 29, 30, 31, 32, 34, 36, 37, 38, 41, 43, 44, 46, 47, 48, 52, 53, 54, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 71, 72, 73, 74, 76, 78, 79, 82, 83, 86, 88, 89, 90, 92, 94, 95, 96, 97, 101, 102, 103, 104, 106, 107, 108, 109, 113, 114, 116, 118, 120, 121

Offset: 1

Author

Antti Karttunen, Mar 10 2019

Keywords

• nonn

Comments

Numbers k for which A324198(k) = 1.

For terms k > 0 it holds that:

A000005(A324580(k)) = A000005(k) * A324655(k),

A000010(A324580(k)) = A000010(k) * A324650(k),

A000203(A324580(k)) = A000203(k) * A324653(k),

and similarly for any multiplicative function.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10001
• Index entries for sequences related to primorial base
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A324584 (complement), A356162 (characteristic function).

Cf. A276086, A324580, A324650, A324653, A324655.

Some subsequences are: A055932 ⊃ A025487 ⊃ A002182, and also A002110.

Subsequence of A356316.

Positions of 1's in A324198, positions 0's in A351254, A356302 and A356303, positions of fixed points in A351250 and in A356309.

Cf. also A355821, A356311.

Programs

PARI

A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A324198(n) = gcd(n,A276086(n));
for(n=0,oo,if(1==A324198(n),print1(n,", ")));

Extensions

Initial 0 prepended by Antti Karttunen, Nov 03 2022