A229335 Sum of sums of elements of subsets of divisors of n.

1, 6, 8, 28, 12, 96, 16, 120, 52, 144, 24, 896, 28, 192, 192, 496, 36, 1248, 40, 1344, 256, 288, 48, 7680, 124, 336, 320, 1792, 60, 9216, 64, 2016, 384, 432, 384, 23296, 76, 480, 448, 11520, 84, 12288, 88, 2688, 2496, 576, 96, 63488, 228, 2976, 576, 3136, 108

Offset: 1

Author

Jaroslav Krizek, Sep 20 2013

Keywords

• nonn

Comments

Number of nonempty subsets of divisors of n = A100587(n).

Examples

			For n = 2^2 = 4; divisors of 4: {1, 2, 4}; nonempty subsets of divisors of n: {1}, {2}, {4}, {1, 2}, {1, 4}, {2, 4}, {1, 2, 4}; sum of sums of elements of subsets = 1 + 2 + 4 + 3 + 5 + 6 + 7 = 28 = (2^3-1) * 2^2 = 7 * 4.
		

Links

• Jaroslav Krizek, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A229336 (product of sums of elements of subsets of divisors of n).

Cf. A229337 (sum of products of elements of subsets of divisors of n).

Cf. A229338 (product of products of elements of subsets of divisors of n).

Programs

Maple

A229335 := proc(n)
    numtheory[sigma](n)*A100577(n) ;
end proc:
seq(A229335(n),n=1..100) ; # R. J. Mathar, Nov 10 2017

Mathematica

Table[Total[Flatten[Subsets[Divisors[n]]]], {n, 100}] (* T. D. Noe, Sep 21 2013 *)

Formula

a(n) = A000203(n) * A100577(n) = A000203(n) * (A100587(n) + 1) / 2 = A000203(n) * 2^(A000005(n) - 1) = sigma(n) * 2^(tau(n) - 1).

a(2^n) = (2^(n+1) - 1) * 2^n.