A347093 Sum of A322577 (convolution of Dedekind psi with Euler phi) and its Dirichlet inverse.

2, 0, 0, 16, 0, 48, 0, 24, 36, 80, 0, 36, 0, 112, 120, 73, 0, 64, 0, 60, 168, 176, 0, 192, 100, 208, 96, 84, 0, 0, 0, 156, 264, 272, 280, 336, 0, 304, 312, 320, 0, 0, 0, 132, 160, 368, 0, 378, 196, 192, 408, 156, 0, 432, 440, 448, 456, 464, 0, 960, 0, 496, 224, 373, 520, 0, 0, 204, 552, 0, 0, 688, 0, 592, 288, 228, 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) = A322577(n) + A347092(n).

For n > 1, a(n) = -Sum_{d|n, 1<d<n} A322577(d) * A347092(n/d).

For all n >= 1, a(A030059(n)) = 0, a(A030229(n)) = 2*A322577(A030229(n)).

Prog

(PARI)
up_to = 16384;
A001615(n) = if(1==n, n, my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1))); \\ After code in A001615
A322577(n) = sumdiv(n, d, A001615(n/d)*eulerphi(d));
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.
v347092 = DirInverseCorrect(vector(up_to, n, A322577(n)));
A347092(n) = v347092[n];
A347093(n) = (A322577(n)+A347092(n));

Crossrefs

Cf. A000010, A001615, A030059, A030229, A322577, A347092, A347094.

Sequence in context: A231246 A216991 A191418 * A347094 A120556 A120560

Adjacent sequences: A347090 A347091 A347092 * A347094 A347095 A347096

Keyword

nonn

Author

Antti Karttunen, Aug 18 2021

Status

approved