A340367 Dirichlet inverse of sequence b(n) = 1-A318833(n).

-1, 0, 0, 2, 0, 7, 0, 6, 6, 13, 0, 13, 0, 19, 22, 10, 0, 19, 0, 23, 32, 31, 0, -3, 20, 37, 24, 33, 0, 21, 0, 6, 52, 49, 58, -36, 0, 55, 62, -9, 0, 29, 0, 53, 52, 67, 0, -87, 42, 53, 82, 63, 0, -29, 94, -15, 92, 85, 0, -219, 0, 91, 74, -22, 112, 45, 0, 83, 112, 45, 0, -257, 0, 109, 82, 93, 136, 53, 0, -165, 42, 121

Offset

1,4

Links

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

Formula

a(1) = -1, for n > 1, a(n) = Sum_{d|n, d<n} (1-A318833(n/d)) * a(d).

Prog

(PARI)
up_to = 65537;
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*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 (correctly!)
A023900(n) = factorback(apply(p -> 1-p, factor(n)[, 1]));
A318833(n) = (n+A023900(n));
v340367 = DirInverseCorrect(vector(up_to, n, 1-A318833(n)));
A340367(n) = v340367[n];
(PARI)
\\ Or as:
A340367(n) = if(1==n, -1, sumdiv(n, d, if(d<n, (1-A318833(n/d))*A340367(d), 0)));

Crossrefs

Cf. A000010, A023900, A318833, A340198.

Cf. also A340140, A340197 for similar definitions.

Sequence in context: A021487 A369745 A197391 * A340197 A340140 A334341

Adjacent sequences: A340364 A340365 A340366 * A340368 A340369 A340370

Keyword

sign

Author

Antti Karttunen, Jan 05 2021

Status

approved