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A346236
Sum of A341530 and its Dirichlet inverse.
5
2, 0, 0, 1, 0, 4, 0, 1, 4, 4, 0, 70, 0, 8, 8, 9, 0, 134, 0, 2, 16, 4, 0, 52, 4, 4, -4, 44, 0, 368, 0, -3, 8, 4, 16, 1037, 0, 8, 8, 18, 0, 352, 0, 6, 460, 12, 0, 564, 16, -2, 8, 34, 0, -296, 8, 344, 16, 4, 0, 464, 0, 4, -8, 29, 8, 160, 0, 2, 24, 736, 0, -395, 0, 4, 460, 20, 16, 200, 0, -14, 21, 4, 0, 2152, 8, 8, 8, 740
OFFSET
1,1
FORMULA
a(n) = A341530(n) + A346235(n).
PROG
(PARI)
up_to = 65537;
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.
A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
A341530(n) = { my(t=A003961(n), s=sigma(t)); gcd((n*s), sigma(n)*t); };
v346235 = DirInverseCorrect(vector(up_to, n, A341530(n)));
A346235(n) = v346235[n];
A346236(n) = (A341530(n)+A346235(n));
CROSSREFS
KEYWORD
sign
AUTHOR
Antti Karttunen, Jul 11 2021
STATUS
approved