cp's OEIS Frontend

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

%I A229335 #10 Nov 10 2017 16:55:52
%S A229335 1,6,8,28,12,96,16,120,52,144,24,896,28,192,192,496,36,1248,40,1344,
%T A229335 256,288,48,7680,124,336,320,1792,60,9216,64,2016,384,432,384,23296,
%U A229335 76,480,448,11520,84,12288,88,2688,2496,576,96,63488,228,2976,576,3136,108
%N A229335 Sum of sums of elements of subsets of divisors of n.
%C A229335 Number of nonempty subsets of divisors of n = A100587(n).
%H A229335 Jaroslav Krizek, <a href="/A229335/b229335.txt">Table of n, a(n) for n = 1..1000</a>
%F A229335 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 A229335 a(2^n)  = (2^(n+1) - 1) * 2^n.
%e A229335 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 A229335 := proc(n)
%p A229335     numtheory[sigma](n)*A100577(n) ;
%p A229335 end proc:
%p A229335 seq(A229335(n),n=1..100) ; # _R. J. Mathar_, Nov 10 2017
%t A229335 Table[Total[Flatten[Subsets[Divisors[n]]]], {n, 100}] (* _T. D. Noe_, Sep 21 2013 *)
%Y A229335 Cf. A229336 (product of sums of elements of subsets of divisors of n).
%Y A229335 Cf. A229337 (sum of products of elements of subsets of divisors of n).
%Y A229335 Cf. A229338 (product of products of elements of subsets of divisors of n).
%K A229335 nonn
%O A229335 1,2
%A A229335 _Jaroslav Krizek_, Sep 20 2013