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A347093
Sum of A322577 (convolution of Dedekind psi with Euler phi) and its Dirichlet inverse.
5
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
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));
KEYWORD
nonn
AUTHOR
Antti Karttunen, Aug 18 2021
STATUS
approved