A354351 - OEIS

%I #14 Jun 08 2022 10:18:18

%S 1,-2,-6,0,-30,12,-210,0,0,60,-2310,0,-30030,420,180,0,-510510,0,

%T -9699690,0,1260,4620,-223092870,0,0,60060,0,0,-6469693230,-360,

%U -200560490130,0,13860,1021020,6300,0,-7420738134810,19399380,180180,0,-304250263527210,-2520,-13082761331670030,0,0,446185740,-614889782588491410

%N Dirichlet inverse of A108951, primorial inflation of n.

%C Multiplicative with a(p^e) = 0 if e > 1, and -A034386(p) otherwise.

%H Antti Karttunen, <a href="/A354351/b354351.txt">Table of n, a(n) for n = 1..2355</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%H <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>

%F a(n) = A008683(n) * A108951(n).

%F a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d < n} A108951(n/d) * a(d).

%F a(n) = A354352(n) - A108951(n).

%o (PARI)

%o A002110(n) = prod(i=1,n,prime(i));

%o A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A002110(primepi(f[i, 1]))^f[i, 2]) }; \\ From A108951

%o A354351(n) = (moebius(n)*A108951(n));

%Y Cf. A002110, A008683,  A013929 (positions of 0's), A034386, A108951, A354352.

%Y Cf. also A347379, A354186, A354349, A354359, A354365, A354366.

%K sign,mult

%O 1,2

%A _Antti Karttunen_, Jun 05 2022