A299163 -id:A299163 - cp's OEIS frontend

A299157 Numbers k such that k+1 divides tau(k), where tau(k) = A000594(k) is Ramanujan's tau function.

2, 3, 5, 6, 7, 11, 13, 17, 19, 20, 22, 23, 27, 29, 31, 41, 45, 47, 53, 55, 59, 68, 71, 76, 77, 79, 83, 87, 89, 91, 97, 104, 107, 114, 127, 137, 139, 149, 160, 167, 171, 177, 179, 183, 191, 195, 199, 209, 223, 229, 239, 240, 243, 251, 269, 275, 293, 297, 321, 343

Offset: 1

Seiichi Manyama, Feb 04 2018

nonn

Numbers k such that A299163(k) = 0.

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

Cf. A000594, A063938, A079334, A296991, A299158, A299163.

q[k_] := Divisible[RamanujanTau[k], k+1]; Select[Range[350], q] (* Amiram Eldar, Jan 08 2025 *)

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

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

Original entry on oeis.org

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)}
```

A299165 a(n) = A000594(n) mod n*(n+1).

Original entry on oeis.org

1, 0, 0, 8, 0, 0, 0, 24, 27, 20, 12, 24, 112, 126, 120, 48, 180, 324, 140, 0, 420, 460, 24, 360, 275, 510, 0, 532, 720, 390, 672, 96, 318, 406, 840, 612, 68, 630, 144, 1480, 1260, 1680, 676, 156, 0, 344, 1296, 1344, 343, 1800, 72, 392, 1566, 540, 2520, 1680

Offset: 1

Seiichi Manyama, Feb 04 2018

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Cf. A000594, A299158, A299163.

a[n_] := Mod[RamanujanTau[n], n*(n+1)]; Array[a, 100] (* Amiram Eldar, Jan 10 2025 *)

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

cp's OEIS Frontend

A299157 Numbers k such that k+1 divides tau(k), where tau(k) = A000594(k) is Ramanujan's tau function.

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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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A299165 a(n) = A000594(n) mod n*(n+1).

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