A323408 Sum of unitary phi and its Dirichlet inverse: a(n) = A047994(n) + A323407(n).

2, 0, 0, 1, 0, 4, 0, 5, 4, 8, 0, 10, 0, 12, 16, 15, 0, 12, 0, 20, 24, 20, 0, 18, 16, 24, 24, 30, 0, 0, 0, 35, 40, 32, 48, 32, 0, 36, 48, 36, 0, 0, 0, 50, 48, 44, 0, 30, 36, 32, 64, 60, 0, 28, 80, 54, 72, 56, 0, 8, 0, 60, 72, 71, 96, 0, 0, 80, 88, 0, 0, 64, 0, 72, 64, 90, 120, 0, 0, 60, 88, 80, 0, 12, 128, 84, 112, 90, 0, 16, 144, 110, 120

Offset

1,1

Links

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

Prog

(PARI)
up_to = 65537;
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.
A047994(n) = { my(f=factor(n)~); prod(i=1, #f, (f[1, i]^f[2, i])-1); };
v323407 = DirInverse(vector(up_to, n, A047994(n)));
A323407(n) = v323407[n];
A323408(n) = (A047994(n) + A323407(n));

Crossrefs

Cf. A047994, A323407.

Cf. also A319340, A322581, A323364, A323399, A323403.

Sequence in context: A319340 A349389 A354876 * A347099 A347239 A347097

Adjacent sequences: A323405 A323406 A323407 * A323409 A323410 A323411

Keyword

nonn

Author

Antti Karttunen, Jan 15 2019

Status

approved