A347095 Sum of Pillai's arithmetical function (A018804) and its Dirichlet inverse.

2, 0, 0, 9, 0, 30, 0, 21, 25, 54, 0, 35, 0, 78, 90, 49, 0, 51, 0, 63, 130, 126, 0, 95, 81, 150, 85, 91, 0, 0, 0, 113, 210, 198, 234, 172, 0, 222, 250, 171, 0, 0, 0, 147, 153, 270, 0, 235, 169, 147, 330, 175, 0, 231, 378, 247, 370, 342, 0, 405, 0, 366, 221, 257, 450, 0, 0, 231, 450, 0, 0, 424, 0, 438, 245, 259, 546

Offset

1,1

Comments

No negative terms in range 1 .. 2^20.

Apparently, A030059 gives the positions of all zeros.

Links

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

Formula

a(n) = A018804(n) + A101035(n).

For n > 1, a(n) = -Sum_{d|n, 1<d<n} A018804(d) * A101035(n/d).

For all n >= 1, a(A030059(n)) = 0, a(A030229(n)) = 2*A018804(A030229(n)).

Prog

(PARI)
up_to = 16384;
A018804(n) = sumdiv(n, d, n*eulerphi(d)/d); \\ From A018804
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.
v101035 = DirInverseCorrect(vector(up_to, n, A018804(n)));
A101035(n) = v101035[n];
A347095(n) = (A018804(n)+A101035(n));

Crossrefs

Cf. A018804, A030059, A030229, A101035.

Cf. also A347094.

Sequence in context: A347085 A347091 A347229 * A346255 A346480 A323399

Adjacent sequences: A347092 A347093 A347094 * A347096 A347097 A347098

Keyword

nonn

Author

Antti Karttunen, Aug 18 2021

Status

approved