A324641 Sum of the Doudna sequence and its Dirichlet inverse: a(n) = A005940(n) + A324640(n).

2, 0, 0, 4, 0, 12, 0, 8, 9, 20, 0, 12, 0, 36, 30, 16, 0, 10, 0, 20, 54, 60, 0, 24, 25, 100, 15, 36, 0, 48, 0, 32, 90, 44, 90, 28, 0, 84, 150, 40, 0, 32, 0, 60, 97, 180, 0, 48, 81, 146, 66, 100, 0, 270, 150, 72, 126, 500, 0, 108, 0, 324, 93, 64, 250, -128, 0, 44, 270, -48, 0, 56, 0, 220, 339, 84, 270, -48, 0, 80, 391, 308, 0, 140, 110

Offset

1,1

Links

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

Formula

a(n) = A005940(n) + A324640(n).

Prog

(PARI)
up_to = 16384;
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.
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ From A005940
v324640 = DirInverse(vector(up_to, n, A005940(n)));
A324640(n) = v324640[n];
A324641(n) = (A005940(n)+A324640(n));

Crossrefs

Sequence in context: A354350 A323884 A061669 * A365804 A349359 A323894

Adjacent sequences: A324638 A324639 A324640 * A324642 A324643 A324644

Keyword

sign

Author

Antti Karttunen, Mar 11 2019

Status

approved