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A354824 Dirichlet inverse of A351084, where A351084(n) = gcd(n, A328572(n)), and A328572 converts the primorial base expansion of n into its prime product form, but with 1 subtracted from all nonzero digits.

%I A354824 #8 Jun 09 2022 11:41:28
%S A354824 1,-1,-1,0,-1,1,-1,0,0,1,-1,0,-1,1,-3,0,-1,0,-1,-4,1,1,-1,0,-24,1,0,0,
%T A354824 -1,7,-1,0,1,1,1,0,-1,1,1,8,-1,-1,-1,0,4,1,-1,0,0,24,1,0,-1,0,-3,0,1,
%U A354824 1,-1,4,-1,1,-6,0,1,-1,-1,0,1,-7,-1,0,-1,1,52,0,-5,-1,-1,-8,0,1,-1,-6,-3,1,1,0,-1,-8,-5,0
%N A354824 Dirichlet inverse of A351084, where A351084(n) = gcd(n, A328572(n)), and A328572 converts the primorial base expansion of n into its prime product form, but with 1 subtracted from all nonzero digits.
%H A354824 Antti Karttunen, <a href="/A354824/b354824.txt">Table of n, a(n) for n = 1..30030</a>
%H A354824 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A354824 a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A351084(n/d) * a(d).
%o A354824 (PARI)
%o A354824 A328572(n) = { my(m=1, p=2); while(n, if(n%p, m *= p^((n%p)-1)); n = n\p; p = nextprime(1+p)); (m); };
%o A354824 A351084(n) = gcd(n, A328572(n));
%o A354824 memoA354824 = Map();
%o A354824 A354824(n) = if(1==n,1,my(v); if(mapisdefined(memoA354824,n,&v), v, v = -sumdiv(n,d,if(d<n,A351084(n/d)*A354824(d),0)); mapput(memoA354824,n,v); (v)));
%Y A354824 Cf. A351084.
%Y A354824 Cf. also A346242, A354347, A354348, A354823.
%K A354824 sign
%O A354824 1,15
%A A354824 _Antti Karttunen_, Jun 09 2022