A355687 - OEIS

%I #9 Jul 15 2022 08:10:57

%S 2,0,0,1,0,4,0,3,4,6,0,4,0,4,12,3,0,-2,0,9,8,8,0,-3,9,6,4,8,0,-10,0,5,

%T 16,10,12,6,0,8,12,-1,0,2,0,14,-2,12,0,12,4,1,20,13,0,14,24,7,16,14,0,

%U -14,0,4,8,3,18,-14,0,11,24,2,0,20,0,6,-10,10,16,-2,0,9,13,10,0,1,30,8,28,-3,0,28,12,16

%N Sum of A276150 and its Dirichlet inverse.

%H Antti Karttunen, <a href="/A355687/b355687.txt">Table of n, a(n) for n = 1..11550</a>

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

%F a(n) = A276150(n) + A355686(n).

%F a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1<d<n} A276150(d) * A355686(n/d).

%o (PARI)

%o A276150(n) = { my(s=0, p=2, d); while(n, d = (n%p); s += d; n = (n-d)/p; p = nextprime(1+p)); (s); };

%o memoA355686 = Map();

%o A355686(n) = if(1==n,1,my(v); if(mapisdefined(memoA355686,n,&v), v, v = -sumdiv(n,d,if(d<n,A276150(n/d)*A355686(d),0)); mapput(memoA355686,n,v); (v)));

%o A355687(n) = (A276150(n)+A355686(n));

%Y Cf. A276150, A355686.

%K sign,base

%O 1,1

%A _Antti Karttunen_, Jul 14 2022