A347094 Sum of A038040 (convolution of sigma with Euler phi) and its Dirichlet inverse.

2, 0, 0, 16, 0, 48, 0, 32, 36, 80, 0, 48, 0, 112, 120, 80, 0, 72, 0, 80, 168, 176, 0, 192, 100, 208, 108, 112, 0, 0, 0, 192, 264, 272, 280, 360, 0, 304, 312, 320, 0, 0, 0, 176, 180, 368, 0, 480, 196, 200, 408, 208, 0, 432, 440, 448, 456, 464, 0, 960, 0, 496, 252, 448, 520, 0, 0, 272, 552, 0, 0, 864, 0, 592, 300, 304, 616

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) = A038040(n) + A328722(n).

For n > 1, a(n) = -Sum_{d|n, 1<d<n} A038040(d) * A328722(n/d).

For all n >= 1, a(A030059(n)) = 0, a(A030229(n)) = 2*A038040(A030229(n)).

Prog

(PARI)
up_to = 16384;
A038040(n) = (n*numdiv(n));
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.
v328722 = DirInverseCorrect(vector(up_to, n, A038040(n)));
A328722(n) = v328722[n];
A347094(n) = (A038040(n)+A328722(n));

Crossrefs

Cf. A000005, A030059, A030229, A038040, A328722, A347093.

Sequence in context: A216991 A191418 A347093 * A120556 A120560 A158465

Adjacent sequences: A347091 A347092 A347093 * A347095 A347096 A347097

Keyword

nonn

Author

Antti Karttunen, Aug 18 2021

Status

approved