A393053 - OEIS

%I #9 Feb 04 2026 09:48:08

%S 1,2,1,3,2,4,2,4,1,2,2,6,2,4,1,5,2,6,2,3,2,4,2,8,1,4,1,6,2,8,2,6,2,4,

%T 2,9,2,4,2,4,2,4,2,6,1,4,2,10,1,2,2,6,2,8,2,4,2,4,2,12,2,4,1,7,4,8,2,

%U 6,2,2,2,12,2,4,1,6,2,8,2,5,1,4,2,6,2,4,2,8,2,12,2,6,2,4,4,12,2,2,2,3,2,8,2,8,1

%N Number of divisors d of n such that d and A276086(n) are coprime, where A276086 is the primorial base exp-function.

%H Antti Karttunen, <a href="/A393053/b393053.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) - A393054(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 A393053(n) = { my(x=A276086(n)); sumdiv(n,d,1==gcd(d,x)); };

%Y Cf. A000005, A276086, A393054.

%Y Cf. also A393051.

%K nonn,base,easy

%O 1,2

%A _Antti Karttunen_, Feb 04 2026