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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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A070563 a(n) = 0 if 3 divides the Ramanujan number tau(n) (A000594(n)), otherwise 1.

Original entry on oeis.org

1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0
Offset: 1

Views

Author

N. J. A. Sloane, May 07 2002

Keywords

Comments

Multiplicative because A000594 is. Conjecture: a(3^k) = 0, if p == 1 mod 3, a(p^2k) = 0 and a(p^(2k+1)) = 1, if p == -1 mod 3, a(p^2k) = 1 and a(p^(2k+1)) = 0. - Christian G. Bower, Jun 10 2005
From Antti Karttunen, Jul 03 2024: (Start)
The above conjecture is not correct. The first counterexample occurs at n = 2401 = 7^4. My improved conjecture is that this is actually a characteristic function of nonmultiples of 3 whose sum of divisors is also a nonmultiple of 3, that is, having a following multiplicative formula: a(3^k) = 0, if p == 1 mod 3, a(p^e) = 1 if e != 2 (mod 3), otherwise 0, and if p == -1 mod 3, a(p^2k) = 1 and a(p^(2k+1)) = 0. This conjecture has now been proved correct by Seiichi Manyama.
Bower's formula is now submitted as A374053.
(End)

Links

Crossrefs

Characteristic function of A374135, nonmultiples of 3 whose sum of divisors is also a nonmultiple of 3.
Cf. A000203, A000594, A011655, A070564, A126825, A353815, A374053.

Programs

Formula

a(n) = A011655(n) * A353815(n), conjectured by Antti Karttunen, proved by Seiichi Manyama, Jul 03 2024
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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