A340189 a(n) = n + A340187(n).

2, 1, 1, 4, 1, 9, 1, 8, 11, 17, 1, 11, 1, 25, 27, 16, 1, 13, 1, 17, 41, 41, 1, 24, 37, 49, 25, 21, 1, 1, 1, 32, 69, 65, 79, 40, 1, 73, 83, 40, 1, -7, 1, 35, 21, 89, 1, 48, 79, 17, 111, 39, 1, 61, 131, 60, 125, 113, 1, 83, 1, 121, 27, 64, 145, -27, 1, 53, 153, -49, 1, 71, 1, 145, 23, 57, 193, -31, 1, 80, 83, 161, 1, 131

Offset

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..8191

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Formula

a(n) = n + A340187(n).

a(n) = A340188(n) + A318828(n).

Prog

(PARI)
up_to = 65537;
A063994(n) = { my(f=factor(n)); prod(i=1, #f~, gcd(f[i, 1]-1, n-1)); };
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.
v340187 = DirInverse(vector(up_to, n, A063994(n)));
A340187(n) = v340187[n];
A340189(n) = (n+A340187(n));

Crossrefs

Cf. A063994, A318828, A340187, A340188.

Cf. also A318833.

Sequence in context: A021477 A124939 A187800 * A323873 A365582 A367559

Adjacent sequences: A340186 A340187 A340188 * A340190 A340191 A340192

Keyword

sign

Author

Antti Karttunen, Dec 31 2020

Status

approved