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.

A346479 Dirichlet inverse of A250469.

Original entry on oeis.org

1, -3, -5, 0, -7, 15, -11, 6, 0, 15, -13, 12, -17, 27, 35, 0, -19, 24, -23, 42, 55, 15, -29, -66, 0, 27, 60, 54, -31, -27, -37, -12, 45, 15, 77, -144, -41, 27, 75, -102, -43, -63, -47, 132, 60, 39, -53, -24, 0, 84, 65, 144, -59, -384, 91, -162, 85, 15, -61, -558, -67, 39, 120, 0, 119, 165, -71, 222, 115, 9, -73, 168
Offset: 1

Views

Author

Antti Karttunen, Jul 30 2021

Keywords

Comments

Not all zeros occur on squares. For example, a(1445) = a(5 * 17^2) = 0.

Links

Crossrefs

Cf. A250469, A346480.
Cf. also A346234, A346477.

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];

Formula

a(1) = 1; and for n > 2, a(n) = -Sum_{d|n, dA250469(n/d).
a(n) = A346480(n) - A250469(n).

A346478 Sum of A346476 and its Dirichlet inverse.

Original entry on oeis.org

2, 0, 0, 1, 0, 2, 0, -3, 1, 6, 0, -11, 0, 6, 6, -5, 0, -23, 0, -29, 6, 18, 0, -3, 9, 18, -15, -37, 0, -60, 0, -9, 18, 30, 18, 23, 0, 30, 18, 1, 0, -84, 0, -83, -61, 34, 0, -13, 9, -67, 30, -91, 0, 45, 54, 5, 30, 54, 0, 75, 0, 50, -77, -5, 54, -184, 0, -137, 34, -176, 0, -13, 0, 66, -55, -145, 54, -188, 0, -37, 49
Offset: 1

Views

Author

Antti Karttunen, Jul 30 2021

Keywords

Links

Crossrefs

Cf. A000040, A000720, A062234, A250469, A252748, A346476, A346477.
Cf. also A323911, A346250, A346480.

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];
A346478(n) = (A346476(n)+A346477(n));

Formula

a(n) = A346476(n) + A346477(n).
a(1) = 2; and for n > 2, a(n) = -Sum_{d|n, 1A346476(n/d) * A346477(d).

A347377 Möbius transform of A280692, A003961(n) - A250469(n).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 6, 0, -6, 0, 12, 0, -6, 0, 30, 0, 24, 0, 12, 0, -24, 0, 48, 0, -24, 60, 24, 0, 24, 0, 114, -20, -42, 0, 84, 0, -42, -10, 60, 0, 48, 0, 12, 60, -48, 0, 168, 0, 6, -30, 24, 0, 132, 0, 108, -30, -78, 0, 96, 0, -72, 120, 390, 0, 44, 0, 12, -30, 36, 0, 288, 0, -96, 60, 24, 0, 58, 0, 228, 360, -114
Offset: 1

Views

Author

Antti Karttunen, Sep 01 2021

Keywords

Links

Crossrefs

Cf. A003961, A003972, A008683, A250469, A280692, A347376.
Cf. also A346480.

Programs

Formula

a(n) = Sum_{d|n} A008683(n/d) * A280692(d).
a(n) = A003972(n) - A347376(n).
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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