cp's OEIS Frontend

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.

Showing 1-3 of 3 results.

A346476 a(n) = 2*n - A250469(n).

Original entry on oeis.org

1, 1, 1, -1, 3, -3, 3, -5, -7, -7, 9, -9, 9, -11, -5, -13, 15, -15, 15, -17, -13, -19, 17, -21, 1, -23, -11, -25, 27, -27, 25, -29, -19, -31, -7, -33, 33, -35, -17, -37, 39, -39, 39, -41, -25, -43, 41, -45, -23, -47, -23, -49, 47, -51, 19, -53, -31, -55, 57, -57, 55, -59, -29, -61, 11, -63, 63, -65, -37
Offset: 1

Views

Author

Antti Karttunen, Jul 29 2021

Keywords

Links

Crossrefs

Cf. A000040, A033879, A062234, A250469, A252748, A280692, A346473, A346477 (Dirichlet inverse), A346478, A347378.

Programs

Formula

a(n) = A280692(n) - A252748(n).
a(n) = A033879(n) - A346473(n).
a(n) = A346478(n) - A346477(n).
a(n) = n - A347378(n).
a(A000040(n)) = -A252748(A000040(n)) = -A346477(A000040(n)) = A062234(n).

A346477 Dirichlet inverse of A346476.

Original entry on oeis.org

1, -1, -1, 2, -3, 5, -3, 2, 8, 13, -9, -2, -9, 17, 11, 8, -15, -8, -15, -12, 19, 37, -17, 18, 8, 41, -4, -12, -27, -33, -25, 20, 37, 61, 25, 56, -33, 65, 35, 38, -39, -45, -39, -42, -36, 77, -41, 32, 32, -20, 53, -42, -47, 96, 35, 58, 61, 109, -57, 132, -55, 109, -48, 56, 43, -121, -63, -72, 71, -109, -69, 56
Offset: 1

Views

Author

Antti Karttunen, Jul 29 2021

Keywords

Links

Crossrefs

Cf. A000040, A000720, A062234, A250469, A252748, A346476, A346478.
Cf. also A323910, A346248, A346479.

Programs

  • PARI
    up_to = 16384;
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(dA346476(n) = (n+n-A250469(n));
v346477 = DirInverseCorrect(vector(up_to,n,A346476(n)));
A346477(n) = v346477[n];

Formula

a(1) = 1; and for n > 2, a(n) = -Sum_{d|n, dA346476(n/d).
a(n) = A346478(n) - A346476(n).
a(p) = A252748(p) = A346248(p) = -A346476(p) = -A062234(A000720(p)), for any prime p.

A346480 Sum of A250469 and its Dirichlet inverse.

Original entry on oeis.org

2, 0, 0, 9, 0, 30, 0, 27, 25, 42, 0, 45, 0, 66, 70, 45, 0, 75, 0, 99, 110, 78, 0, 3, 49, 102, 125, 135, 0, 60, 0, 81, 130, 114, 154, -39, 0, 138, 170, 15, 0, 60, 0, 261, 175, 174, 0, 117, 121, 231, 190, 297, 0, -225, 182, 3, 230, 186, 0, -381, 0, 222, 275, 189, 238, 360, 0, 423, 290, 216, 0, 381, 0, 246, 245, 459
Offset: 1

Views

Author

Antti Karttunen, Jul 30 2021

Keywords

Links

Crossrefs

Cf. A250469, A346479.
Cf. also A346478.

Programs

  • PARI
    up_to = 16384;
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(dA250469(n)));
A346479(n) = v346479[n];
A346480(n) = (A250469(n)+A346479(n));
  • PARI
    A346480(n) = if(1==n, 2, -sumdiv(n,d,if((1==d)||n==d,0,A250469(d)*A346479(n/d)))); \\ (Demonstrates the convolution formula).

Formula

a(n) = A250469(n) + A346479(n).
a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1A250469(d) * A346479(n/d).
Showing 1-3 of 3 results.

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