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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A378453 Dirichlet inverse of A018892, where A018892(n) = (tau(n^2)+1)/2.

Original entry on oeis.org

1, -2, -2, 1, -2, 3, -2, 0, 1, 3, -2, 0, -2, 3, 3, 0, -2, 0, -2, 0, 3, 3, -2, -1, 1, 3, 0, 0, -2, -2, -2, 0, 3, 3, 3, -2, -2, 3, 3, -1, -2, -2, -2, 0, 0, 3, -2, 0, 1, 0, 3, 0, -2, -1, 3, -1, 3, 3, -2, -3, -2, 3, 0, 0, 3, -2, -2, 0, 3, -2, -2, 0, -2, 3, 0, 0, 3, -2, -2, 0, 0, 3, -2, -3, 3, 3, 3, -1, -2, -3, 3, 0, 3, 3, 3
Offset: 1

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Author

Antti Karttunen, Nov 29 2024

Keywords

Comments

Möbius transform of A378452.

Links

Crossrefs

Cf. A008683, A018892, A378452.

Programs

  • PARI
    A018892(n) = ((numdiv(n^2)+1)/2);
memoA378453 = Map();
A378453(n) = if(1==n,1,my(v); if(mapisdefined(memoA378453,n,&v), v, v = -sumdiv(n,d,if(dA018892(n/d)*A378453(d),0)); mapput(memoA378453,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA018892(n/d) * a(d).
a(n) = Sum_{d|n} A008683(n/d)*A378452(d).
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