A372568 - OEIS

%I #7 May 24 2024 14:38:41

%S 1,0,-2,0,0,2,0,0,4,-4,0,0,0,0,-12,0,0,-8,0,0,0,0,0,0,-24,0,-8,0,0,32,

%T 0,0,0,0,-6,4,0,0,0,0,0,-6,0,0,48,0,0,0,-6,4,0,0,0,24,-4,-6,0,0,0,-16,

%U 0,0,-18,0,0,0,0,0,0,-24,0,0,0,0,60,0,-6,0,0,0,16,0,0,0,-4,0,0,0,0,-160,-6,0,0,0,0,0,0,-42

%N a(n) = Sum_{d|n} A346242(d), where A346242 is the Dirichlet inverse of gcd(n, A276086(n)).

%C No odd terms after the initial 1.

%H Antti Karttunen, <a href="/A372568/b372568.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>

%o (PARI)

%o A324198(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)); (m); };

%o memoA346242 = Map();

%o A346242(n) = if(1==n,1,my(v); if(mapisdefined(memoA346242,n,&v), v, v = -sumdiv(n,d,if(d<n,A324198(n/d)*A346242(d),0)); mapput(memoA346242,n,v); (v)));

%o A372568(n) = sumdiv(n,d,A346242(d));

%Y Inverse Möbius transform of A346242.

%Y Cf. A276086, A324198.

%K sign

%O 1,3

%A _Antti Karttunen_, May 24 2024