A273650 - OEIS

%I #30 Jan 09 2025 02:05:23

%S 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,

%T 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,

%U 14,0,49,54,0,0,30,24,64,36,45,0,19,0,67,70,0,32,42,54,37,0,0,18

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

%H Seiichi Manyama, <a href="/A273650/b273650.txt">Table of n, a(n) for n = 1..10000</a>

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

%F From _Amiram Eldar_, Jan 08 2025: (Start)

%F a(A063938(n)) = 0.

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

%e tau(10) mod 10 = (-115920) mod 10 = 0,

%e tau(11) mod 11 = 534612 mod 11 = 1.

%t a[n_] := Mod[RamanujanTau[n], n]; Array[a, 100] (* _Amiram Eldar_, Jan 08 2025 *)

%o (PARI) a(n)=ramanujantau(n)%n \\ assumes the GRH; _Charles R Greathouse IV_, May 27 2016

%o (Python)

%o from sympy import divisor_sigma

%o 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

%Y Cf. A000594, A063938, A295654.

%K nonn,changed

%O 1,13

%A _Seiichi Manyama_, May 27 2016