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.

A359427 Dirichlet inverse of A358764.

Original entry on oeis.org

1, -2, -3, -2, -9, 8, -5, 6, -6, 6, -45, -4, -25, -30, -21, -130, -225, -70, -125, -130, -345, -570, -1125, -480, -544, -1150, -1812, -3550, -5625, 222, -7, 530, 249, 858, 27, 418, -35, 430, 45, 610, -315, 1520, -175, 2650, -48, 3450, -1575, 2060, -850, 804, -1275, -250, -7875, 4288, -3565, 6150, -12375
Offset: 1

Views

Author

Antti Karttunen, Jan 02 2023

Keywords

Links

Crossrefs

Cf. A060681, A276086, A358764, A359428.
Cf. A056911 (positions of odd terms), A323239 (parity of terms), A337945.
Cf. also A342417.

Programs

  • PARI
    up_to = 11550;
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(dA032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
A060681(n) = (n-A032742(n));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A358764(n) = A060681(A276086(n));
v359427 = DirInverseCorrect(vector(up_to,n,A358764(n)));
A359427(n) = v359427[n];

Formula

a(n) = A359428(n) - A358764(n).

A359428 Sum of A358764 and its Dirichlet inverse.

Original entry on oeis.org

2, 0, 0, 4, 0, 12, 0, 16, 9, 36, 0, 16, 0, 20, 54, 20, 0, 30, 0, 120, 30, 180, 0, 20, 81, 100, 63, 200, 0, 228, 0, 544, 270, 900, 90, 446, 0, 500, 150, 820, 0, 1660, 0, 3000, 477, 4500, 0, 2760, 25, 2554, 1350, 5000, 0, 7788, 810, 14900, 750, 22500, 0, 936, 0, 28, 2265, -12, 450, 3324, 0, 168, 6750
Offset: 1

Views

Author

Antti Karttunen, Jan 02 2023

Keywords

Links

Crossrefs

Cf. A060681, A276086, A358764, A359427.
Cf. A053850 (positions of odd terms), A353569 (parity of terms).
Cf. also A342419.

Programs

Formula

a(n) = A358764(n) + A359427(n).
a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1A358764(d) * A359427(n/d).

A359426 a(n) = A342001(A358764(n)).

Original entry on oeis.org

0, 1, 1, 5, 2, 2, 1, 7, 8, 31, 13, 12, 2, 9, 11, 37, 16, 14, 3, 11, 14, 43, 19, 16, 4, 13, 17, 49, 22, 5, 1, 9, 10, 41, 17, 16, 12, 59, 71, 247, 106, 94, 19, 73, 92, 289, 127, 108, 26, 87, 113, 331, 148, 122, 33, 101, 134, 373, 169, 41, 2, 11, 13, 47, 20, 18, 17, 69, 86, 277, 121, 104, 24, 83, 107
Offset: 1

Views

Author

Antti Karttunen, Jan 02 2023

Keywords

Comments

Variant of A342002.

Links

Crossrefs

Cf. A276086, A342001, A358764.
Cf. also A342002.

Programs

Showing 1-3 of 3 results.

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

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