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

%I A324583 #28 Nov 04 2022 11:26:03
%S A324583 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,
%T A324583 34,36,37,38,41,43,44,46,47,48,52,53,54,58,59,60,61,62,64,65,66,67,68,
%U A324583 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
%N A324583 Numbers k such that k and A276086(k) are coprime, where A276086 is the primorial base exp-function.
%C A324583 Numbers k for which A324198(k) = 1.
%C A324583 For terms k > 0 it holds that:
%C A324583   A000005(A324580(k)) = A000005(k) * A324655(k),
%C A324583   A000010(A324580(k)) = A000010(k) * A324650(k),
%C A324583   A000203(A324580(k)) = A000203(k) * A324653(k),
%C A324583 and similarly for any multiplicative function.
%H A324583 Antti Karttunen, <a href="/A324583/b324583.txt">Table of n, a(n) for n = 1..10001</a>
%H A324583 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%H A324583 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%o A324583 (PARI)
%o A324583 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A324583 A324198(n) = gcd(n,A276086(n));
%o A324583 for(n=0,oo,if(1==A324198(n),print1(n,", ")));
%Y A324583 Cf. A324584 (complement), A356162 (characteristic function).
%Y A324583 Cf. A276086, A324580, A324650, A324653, A324655.
%Y A324583 Some subsequences are: A055932 ⊃ A025487 ⊃ A002182, and also A002110.
%Y A324583 Subsequence of A356316.
%Y A324583 Positions of 1's in A324198, positions 0's in A351254, A356302 and A356303, positions of fixed points in A351250 and in A356309.
%Y A324583 Cf. also A355821, A356311.
%K A324583 nonn
%O A324583 1,3
%A A324583 _Antti Karttunen_, Mar 10 2019
%E A324583 Initial 0 prepended by _Antti Karttunen_, Nov 03 2022