A355692 - OEIS

%I #8 Jul 18 2022 16:39:17

%S 1,-3,-1,0,-1,1,-1,24,-4,3,-1,16,-1,3,-3,-72,-1,6,-1,6,-3,3,-1,-68,0,

%T 3,-116,0,-1,21,-1,24,1,3,-5,72,-1,3,-3,-120,-1,23,-1,6,-158,3,-1,28,

%U 0,-18,-3,0,-1,632,-5,-24,-3,3,-1,-54,-1,3,16,504,-5,-1,-1,6,-3,15,-1,-400,-1,3,-236,0,1,23,-1,474,136

%N Dirichlet inverse of A355442, gcd(A003961(n), A276086(n)), where A003961 is fully multiplicative with a(p) = nextprime(p), and A276086 is primorial base exp-function.

%H Antti Karttunen, <a href="/A355692/b355692.txt">Table of n, a(n) for n = 1..11550</a>

%H Antti Karttunen, <a href="/A355692/a355692.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

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

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

%F a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A355442(n/d) * a(d).

%o (PARI)

%o A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

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

%o A355442(n) = gcd(A003961(n), A276086(n));

%o memoA355692 = Map();

%o A355692(n) = if(1==n,1,my(v); if(mapisdefined(memoA355692,n,&v), v, v = -sumdiv(n,d,if(d<n,A355442(n/d)*A355692(d),0)); mapput(memoA355692,n,v); (v)));

%Y Cf. A003961, A276086.

%Y Cf. also A346242, A354347, A354348, A354823, A354824.

%K sign

%O 1,2

%A _Antti Karttunen_, Jul 18 2022