A229335 - OEIS

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

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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: A374120 A267477 A237290 * A007829 A345003 A000773

Adjacent sequences: A229332 A229333 A229334 * A229336 A229337 A229338

KEYWORD

nonn

AUTHOR

Jaroslav Krizek, Sep 20 2013

STATUS

approved