A393054 - OEIS

%I #9 Feb 04 2026 09:48:17

%S 0,0,1,0,0,0,0,0,2,2,0,0,0,0,3,0,0,0,0,3,2,0,0,0,2,0,3,0,0,0,0,0,2,0,

%T 2,0,0,0,2,4,0,4,0,0,5,0,0,0,2,4,2,0,0,0,2,4,2,0,0,0,0,0,5,0,0,0,0,0,

%U 2,6,0,0,0,0,5,0,2,0,0,5,4,0,0,6,2,0,2,0,0,0,2,0,2,0,0,0,0,4,4,6,0,0,0,0,7

%N Number of divisors d of n such that d and A276086(n) are not coprime, where A276086 is the primorial base exp-function.

%H Antti Karttunen, <a href="/A393054/b393054.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>.

%F a(n) = Sum_{d|n} [gcd(d,A276086(n)) > 1], where [ ] is the Iverson bracket.

%F a(n) = A000005(n) - A393053(n).

%o (PARI)

%o A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };

%o A393054(n) = { my(x=A276086(n)); sumdiv(n,d,1!=gcd(d,x)); };

%Y Cf. A000005, A276086, A393053.

%Y Cf. also A393052.

%K nonn,base,easy

%O 1,9

%A _Antti Karttunen_, Feb 04 2026