A299172 -id:A299172 - cp's OEIS frontend

A299171 Primes p such that Ramanujan number tau(p) is divisible by p+1.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 53, 59, 71, 79, 83, 89, 97, 107, 127, 137, 139, 149, 167, 179, 191, 199, 223, 229, 239, 251, 269, 293, 349, 359, 367, 383, 419, 431, 449, 479, 499, 503, 587, 593, 599, 643, 647, 719, 809, 827, 839, 863, 881, 919

Offset: 1

Seiichi Manyama, Feb 04 2018

nonn

Amiram Eldar, Table of n, a(n) for n = 1..900

Cf. A000594, A007659, A299157, A299163, A299172.

Select[Range[1000], PrimeQ[#] && Divisible[RamanujanTau[#], #+1] &] (* Amiram Eldar, Apr 14 2021 *)

isok(p) = isprime(p) && !(ramanujantau(p) % (p+1)); \\ Michel Marcus, Feb 05 2018

A299204 a(n) = A000594(n) mod (n-1).

Original entry on oeis.org

0, 0, 1, 2, 2, 2, 4, 5, 0, 2, 9, 2, 0, 0, 1, 2, 3, 2, 2, 12, 18, 10, 22, 7, 12, 22, 2, 2, 5, 2, 11, 16, 15, 2, 31, 2, 12, 32, 3, 2, 8, 2, 27, 42, 27, 22, 9, 9, 16, 32, 32, 10, 33, 18, 0, 0, 30, 0, 29, 2, 38, 50, 28, 20, 39, 26, 48, 48, 0, 2, 4, 2, 5, 26, 35, 12

Offset: 2

Seiichi Manyama, Feb 05 2018

nonn

Seiichi Manyama, Table of n, a(n) for n = 2..10000

Cf. A000594, A273650, A299163, A299172, A299205.

f[n_] := Mod[RamanujanTau@n, n - 1]; Array[f, 76, 2] (* Robert G. Wilson v, Feb 07 2018 *)

PARI
```
{a(n) = ramanujantau(n)%(n-1)}
```

A299205 Numbers k such that k-1 divides tau(k), where tau(k) = A000594(k) is Ramanujan's tau function.

Original entry on oeis.org

2, 3, 10, 14, 15, 56, 57, 59, 70, 85, 105, 107, 116, 136, 209, 267, 295, 323, 352, 393, 415, 442, 530, 551, 645, 646, 760, 855, 1197, 1288, 1342, 1415, 1472, 1496, 1625, 1765, 1953, 2002, 2255, 2485, 2847, 2945, 3039, 3382, 3591, 3745, 3905, 4233, 4264, 4313

Offset: 1

Seiichi Manyama, Feb 05 2018

nonn

Numbers k such that A299204(k) = 0.

Seiichi Manyama, Table of n, a(n) for n = 1..500
Eric Weisstein's World of Mathematics, Tau Function.

For the sequence when n is prime see A299172.

Cf. A000594, A063938, A299157, A299204.

Select[Range[2, 5000], Divisible[RamanujanTau[#], #-1] &] (* Amiram Eldar, Jan 10 2025 *)

isok(n) = (ramanujantau(n) % (n-1)) == 0; \\ Michel Marcus, Feb 05 2018

cp's OEIS Frontend

A299171 Primes p such that Ramanujan number tau(p) is divisible by p+1.

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A299204 a(n) = A000594(n) mod (n-1).

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Author

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Mathematica

PARI

A299205 Numbers k such that k-1 divides tau(k), where tau(k) = A000594(k) is Ramanujan's tau function.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI