A323900 Sum of A287896 and its Dirichlet inverse.

2, 0, 0, 4, 0, 8, 0, 4, 4, 12, 0, 4, 0, 12, 12, 5, 0, 8, 0, 6, 12, 20, 0, 8, 9, 20, 8, 6, 0, -8, 0, 6, 20, 20, 18, 12, 0, 28, 20, 12, 0, 8, 0, 10, 4, 28, 0, 10, 9, 10, 20, 10, 0, 16, 30, 12, 28, 28, 0, 20, 0, 20, 20, 7, 30, -16, 0, 10, 28, 0, 0, 16, 0, 44, -2, 14, 30, 0, 0, 15, 16, 44, 0, 28, 30, 52, 28, 20, 0, 40

Offset: 1

Author

Antti Karttunen, Feb 12 2019

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A001511, A002487, A287896, A323365, A323885, A323899.

Programs

PARI

up_to = 20000;
DirInverse(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = -sumdiv(n, d, if(dA001511(n) = (1+valuation(n,2));
A002487(n) = { my(a=1, b=0); while(n>0, if(bitand(n, 1), b+=a, a+=b); n>>=1); (b); }; \\ From A002487
A287896(n) = (A001511(n)*A002487(n));
v323899 = DirInverse(vector(up_to,n,A287896(n)));
A323899(n) = v323899[n];
A323900(n) = (A287896(n)+A323899(n));

Formula

a(n) = A287896(n) + A323899(n).