A346104 Dirichlet inverse of A342920.

1, -1, -1, -1, -1, 0, -1, -5, -11, 0, -1, 1, -1, 0, -4, -1, -1, 1, -1, 1, -4, 0, -1, -8, -49, 0, 7, 1, -1, -48, -1, 25, -4, 0, -124, 12, -1, 0, -4, 0, -1, -10, -1, 1, -13, 0, -1, 41, -1485, 1, -4, 1, -1, 22, -92, 10, -4, 0, -1, 76, -1, 0, -39, 23, -262, 2, -1, 1, -4, 134, -1, -138, -1, 0, -1033, 1, -240, 2, -1, 11, -201, 0, -1, 6

Offset

1,8

Comments

The lowermost scatter plot gives an appearance of an elliptic galaxy seen from its side.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences related to primorial base

Index entries for sequences related to primorial numbers

Prog

(PARI)
up_to = 2310;
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!)
A034386(n) = prod(i=1, primepi(n), prime(i));
A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) };  \\ From A108951
A342002(n) = { my(s=0, m=1, p=2, e); while(n, e = (n%p); m *= p^(e>0); s += (e/p); n = n\p; p = nextprime(1+p)); (s*m); };
A342920(n) = A342002(A108951(n));
v346104 = DirInverseCorrect(vector(up_to, n, A342920(n)));
A346104(n) = v346104[n];

Crossrefs

Cf. A108951, A324886, A342001, A342002, A342920, A346103.

Cf. also A342417.

Sequence in context: A201026 A213146 A309558 * A087463 A160366 A160923

Adjacent sequences: A346101 A346102 A346103 * A346105 A346106 A346107

Keyword

sign,look

Author

Antti Karttunen, Jul 09 2021

Status

approved