|
%I #18 Nov 06 2023 03:21:59
%S 0,0,1,0,0,16,1,0,81,0,1,256,0,16,626,0,0,1296,1,0,2482,16,1,4096,0,0,
%T 6562,256,0,10016,1,0,14722,0,626,20736,0,16,28562,0,0,39712,1,256,
%U 50706,16,1,65536,2401,0,83522,0,0,104992,626,4096,130402
%N a(n) = Sum_{d|n, n/d=3 mod 4} d^4.
%H Amiram Eldar, <a href="/A050467/b050467.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harvey P. Dale)
%F From _Amiram Eldar_, Nov 05 2023: (Start)
%F a(n) = A285989(n) - A050463(n).
%F a(n) = A050463(n) - A050468(n).
%F a(n) = (A285989(n) - A050468(n))/2.
%F Sum_{k=1..n} a(k) ~ c * n^5 / 5, where c = 31*zeta(5)/64 - 5*Pi^5/3072 = 0.00418296735902... . (End)
%t Table[Total[Select[Divisors[n],Mod[n/#,4]==3&]^4],{n,60}] (* _Harvey P. Dale_, Jun 10 2023 *)
%t a[n_] := DivisorSum[n, #^4 &, Mod[n/#, 4] == 3 &]; Array[a, 50] (* _Amiram Eldar_, Nov 05 2023 *)
%o (PARI) a(n) = sumdiv(n, d, (n/d % 4 == 3) * d^4); \\ _Amiram Eldar_, Nov 05 2023
%Y Cf. A013663, A050463, A050468, A285989.
%Y Cf. A050464, A050465, A050466.
%K nonn,easy
%O 1,6
%A _N. J. A. Sloane_, Dec 23 1999
%E Offset corrected by _Amiram Eldar_, Nov 05 2023
|
