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 A229335 Sum of sums of elements of subsets of divisors of n. 10
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Number of nonempty subsets of divisors of n = A100587(n). LINKS Jaroslav Krizek, Table of n, a(n) for n = 1..1000 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. EXAMPLE 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. 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 *) 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). Sequence in context: A066231 A267477 A237290 * A007829 A000773 A258283 Adjacent sequences:  A229332 A229333 A229334 * A229336 A229337 A229338 KEYWORD nonn AUTHOR Jaroslav Krizek, Sep 20 2013 STATUS approved

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Last modified February 28 01:38 EST 2020. Contains 332319 sequences. (Running on oeis4.)