A366607 Sum of the divisors of 4^n+1.

3, 6, 18, 84, 258, 1302, 4356, 20520, 65538, 351120, 1110276, 5048232, 17041416, 82623888, 284225796, 1494039792, 4301668356, 20788904016, 73234343952, 332019460560, 1103789883396, 5936210280000, 18679788287496, 84884999116320, 282937726148616

Offset: 0

Author

Sean A. Irvine, Oct 14 2023

Keywords

• nonn

Examples

			a(3)=84 because 4^3+1 has divisors {1, 5, 13, 65}.
		

Links

• Max Alekseyev, Table of n, a(n) for n = 0..583

Crossrefs

Cf. A000203, A052539, A057940, A274903, A366603, A366605, A366606, A366608, A366609.

Cf. A069061, A366578, A366617, A366629, A366638, A366657, A366666, A366668, A366689, A366715.

Programs

Maple

a:=n->numtheory[sigma](4^n+1):
seq(a(n), n=0..100);

Mathematica

DivisorSigma[1,4^Range[0,30]+1] (* Paolo Xausa, Oct 14 2023 *)

Python

from sympy import divisor_sigma
def A366607(n): return divisor_sigma((1<<(n<<1))+1) # Chai Wah Wu, Oct 14 2023

Formula

a(n) = sigma(4^n+1) = A000203(A052539(n)).

a(n) = A069061(2*n). - Max Alekseyev, Jan 08 2024