A273650 a(n) = A000594(n) mod n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 8, 0, 0, 0, 10, 0, 7, 0, 0, 20, 1, 0, 0, 16, 0, 0, 24, 0, 21, 0, 21, 32, 0, 0, 31, 22, 27, 0, 30, 0, 31, 24, 0, 22, 27, 0, 0, 0, 21, 28, 29, 0, 45, 0, 54, 4, 14, 0, 49, 54, 0, 0, 30, 24, 64, 36, 45, 0, 19, 0, 67, 70, 0, 32, 42, 54, 37, 0, 0, 18

Offset

1,13

Links

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

Formula

a(n) = A000594(n) mod n.

From Amiram Eldar, Jan 08 2025: (Start)

a(A063938(n)) = 0.

abs(a(A295654(n))) = 1. (End)

Example

tau(10) mod 10 = (-115920) mod 10 = 0,
tau(11) mod 11 = 534612 mod 11 = 1.

Mathematica

a[n_] := Mod[RamanujanTau[n], n]; Array[a, 100] (* Amiram Eldar, Jan 08 2025 *)

Prog

(PARI) a(n)=ramanujantau(n)%n \\ assumes the GRH; Charles R Greathouse IV, May 27 2016
(Python)
from sympy import divisor_sigma
def A273650(n): return -840*(pow(m:=n+1>>1, 2, n)*(0 if n&1 else pow(m*divisor_sigma(m), 2, n))+(sum(pow(i, 4, n)*divisor_sigma(i)*divisor_sigma(n-i) for i in range(1, m))<<1)) % n # Chai Wah Wu, Nov 08 2022

Crossrefs

Cf. A000594, A063938, A295654.

Sequence in context: A317445 A199619 A036482 * A263014 A028721 A028664

Adjacent sequences: A273647 A273648 A273649 * A273651 A273652 A273653

Keyword

nonn

Author

Seiichi Manyama, May 27 2016

Status

approved