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

Author

Antti Karttunen, Aug 18 2021

Keywords

• nonn

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

Crossrefs

Cf. A018804, A030059, A030229, A101035.

Cf. also A347094.

Programs

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(dA018804(n)));
A101035(n) = v101035[n];
A347095(n) = (A018804(n)+A101035(n));

Formula

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

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

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