A356154 - OEIS

%I #7 Jul 28 2022 21:15:56

%S 1,-1,-2,0,-1,3,-1,0,3,1,-1,-1,-1,1,3,0,-1,-7,-1,-1,2,1,-1,0,-1,1,-5,

%T 0,-1,-5,-1,0,3,1,1,5,-1,1,2,2,-1,-3,-1,0,-7,1,-1,0,-4,2,3,0,-1,15,1,

%U -3,2,1,-1,5,-1,1,-3,0,1,-5,-1,0,3,-1,-1,-2,-1,1,2,0,-1,-3,-1,-1,8,1,-1,1,1,1,3,0,-1,17

%N Dirichlet inverse of A356153.

%H Antti Karttunen, <a href="/A356154/b356154.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(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A356153(n/d) * a(d).

%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 A356153(n) = for(k=1, oo, if((k*A276086(k))%n==0, return(k/gcd(n,k))));

%o memoA356154 = Map();

%o A356154(n) = if(1==n,1,my(v); if(mapisdefined(memoA356154,n,&v), v, v = -sumdiv(n,d,if(d<n,A356153(n/d)*A356154(d),0)); mapput(memoA356154,n,v); (v)));

%Y Cf. A276086, A355944, A356151, A356153.

%K sign

%O 1,3

%A _Antti Karttunen_, Jul 28 2022