A244824 Sum of all divisors of all positive integers <= 2^n.

1, 4, 15, 56, 220, 857, 3403, 13535, 54077, 215900, 862954, 3450545, 13802279, 55201838, 220792018, 883134861, 3532518195, 14129951284, 56519699688, 226078355122, 904312961284, 3617249936000, 14468996179294, 57875977567596, 231503907383054, 926015589350438

Offset: 0

Author

Omar E. Pol, Jul 06 2014

Keywords

• nonn

Comments

Has a symmetric representation, the same as A024916.

Examples

			For n = 2 the sum of all divisors of all positive integers <= 4 is [1] + [1+2] + [1+3] + [1+2+4] = 1 + 3 + 4 + 7 = 15, so a(2) = 15.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..75

Crossrefs

Cf. A000079, A000203, A024916, A196020, A235796, A236104, A237270, A237593.

Programs

PARI

a(n) = sum(k=1, 2^n, k*floor(2^n/k) ) \\ Jens Kruse Andersen, Jul 26 2014

Python

from math import isqrt
def A244824(n): return -(s:=isqrt(m:=1<>1 # Chai Wah Wu, Oct 23 2023

Formula

a(n) = A024916(A000079(n)).

a(n) ~ 2^(2*n-2) * Pi^2/3. - Vaclav Kotesovec, Oct 23 2023

Extensions

More terms from Jens Kruse Andersen, Jul 26 2014