login
Sum of sums of elements of subsets of divisors of n.
10

%I #10 Nov 10 2017 16:55:52

%S 1,6,8,28,12,96,16,120,52,144,24,896,28,192,192,496,36,1248,40,1344,

%T 256,288,48,7680,124,336,320,1792,60,9216,64,2016,384,432,384,23296,

%U 76,480,448,11520,84,12288,88,2688,2496,576,96,63488,228,2976,576,3136,108

%N Sum of sums of elements of subsets of divisors of n.

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

%H Jaroslav Krizek, <a href="/A229335/b229335.txt">Table of n, a(n) for n = 1..1000</a>

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

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

%e 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.

%p A229335 := proc(n)

%p numtheory[sigma](n)*A100577(n) ;

%p end proc:

%p seq(A229335(n),n=1..100) ; # _R. J. Mathar_, Nov 10 2017

%t Table[Total[Flatten[Subsets[Divisors[n]]]], {n, 100}] (* _T. D. Noe_, Sep 21 2013 *)

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

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

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

%K nonn

%O 1,2

%A _Jaroslav Krizek_, Sep 20 2013