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

Author

Seiichi Manyama, May 27 2016

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Cf. A000594, A063938, A295654.

Programs

Mathematica

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

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

Formula

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

From Amiram Eldar, Jan 08 2025: (Start)

a(A063938(n)) = 0.

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