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

1,1

Links

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

Formula

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

Prog

(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(d<n, v[n/d]*u[d], 0))); (u) }; \\ Compute the Dirichlet inverse of the sequence given in input vector v.
A001511(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));

Crossrefs

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

Sequence in context: A221419 A140668 A353369 * A349347 A354187 A349345

Adjacent sequences: A323897 A323898 A323899 * A323901 A323902 A323903

Keyword

sign

Author

Antti Karttunen, Feb 12 2019

Status

approved