A319528 a(n) = 8 * sigma(n).

8, 24, 32, 56, 48, 96, 64, 120, 104, 144, 96, 224, 112, 192, 192, 248, 144, 312, 160, 336, 256, 288, 192, 480, 248, 336, 320, 448, 240, 576, 256, 504, 384, 432, 384, 728, 304, 480, 448, 720, 336, 768, 352, 672, 624, 576, 384, 992, 456, 744, 576, 784, 432, 960, 576, 960, 640, 720, 480, 1344, 496, 768, 832

Offset: 1

Author

Omar E. Pol, Sep 22 2018

Keywords

• nonn
• easy

Comments

8 times the sum of the divisors of n.

a(n) is also the total number of horizontal rhombuses in the terraces of the n-th level of an irregular stepped pyramid (starting from the top) in which the structure of every 45-degree three-dimensional sector arises after the 45-degree zig-zag folding of every row of the diagram of the isosceles triangle A237593. The top of the pyramid is an eight-pointed star formed by eight rhombuses (see Links section).

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..10000
• Omar E. Pol, Diagram of the triangle A237593 before the 45-degree-zig-zag folding (rows: 1..28)
• Index entries for sequences related to sigma(n)

Crossrefs

k times sigma(n), k=1..7: A000203, A074400, A272027, A239050, A274535, A274536, A319527.

Cf. A008589, A047304, A237593, A283078.

Programs

GAP

List([1..70],n->8*Sigma(n)); # Muniru A Asiru, Sep 28 2018

Maple

with(numtheory): seq(8*sigma(n), n=1..64);

Mathematica

8*DivisorSigma[1,Range[70]] (* Harvey P. Dale, Dec 24 2018 *)

PARI

a(n) = 8 * sigma(n);

Formula

a(n) = 8*A000203(n) = 4*A074400(n) = 2*A239050(n).

a(n) = A000203(n) + A319527(n).

Dirichlet g.f.: 8*zeta(s-1)*zeta(s). (After Ilya Gutkovskiy)

Conjecture: a(n) = sigma(7*n) = A283078(n) iff n is not a multiple of 7.

Conjecture is true, since sigma is multiplicative, so if (7,n) = 1 then sigma(7*n) = sigma(7)*sigma(n) = 8*sigma(n). - Charlie Neder, Oct 02 2018