A393051 - OEIS

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

%S 1,2,1,3,2,3,2,4,1,3,2,5,2,4,2,5,2,4,2,4,2,4,2,7,2,4,1,6,2,5,2,6,2,4,

%T 3,7,2,4,2,5,2,5,2,6,2,4,2,9,2,3,2,6,2,5,3,7,2,4,2,8,2,4,2,7,4,6,2,6,

%U 2,5,2,10,2,4,2,6,3,6,2,6,1,4,2,8,3,4,2,8,2,7,3,6,2,4,4,11,2,4,2,4,2,6,2,8,3

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

%C Number of nonzero terms of A324583 that divide n.

%H Antti Karttunen, <a href="/A393051/b393051.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} A356162(d).

%F a(n) = A000005(n) - A393052(n).

%F a(n) >= A322584(n).

%o (PARI)

%o A356162(n) = { my(m=1, p=2, orgn=n); while(n, m *= (p^min(n%p, valuation(orgn, p))); n = n\p; p = nextprime(1+p)); (1==m); };

%o A393051(n) = sumdiv(n,d,A356162(d));

%Y Inverse Möbius transform of A356162.

%Y Cf. A000005, A324583, A393052.

%Y Cf. also A322584, A393053.

%K nonn,base,easy

%O 1,2

%A _Antti Karttunen_, Feb 04 2026