

A319528


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


10



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
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OFFSET

1,1


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 nth level of an irregular stepped pyramid (starting from the top) in which the structure of every 45degreethreedimensional sector arises after the 45degreezigzag folding of every row of the diagram of the isosceles triangle A237593. The top of the pyramid is a eightpointed 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 45degreezigzag folding (rows: 1..28)
Index entries for sequences related to 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(s1)*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


MAPLE

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


MATHEMATICA

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


PROG

(PARI) a(n) = 8 * sigma(n);
(GAP) List([1..70], n>8*Sigma(n)); # Muniru A Asiru, Sep 28 2018


CROSSREFS

k times sigma(n), k=1..7: A000203, A074400, A272027, A239050, A274535, A274536, A319527.
Cf. A008589, A047304, A237593, A283078.
Sequence in context: A333427 A128690 A283078 * A140403 A108578 A305241
Adjacent sequences: A319525 A319526 A319527 * A319529 A319530 A319531


KEYWORD

nonn,easy


AUTHOR

Omar E. Pol, Sep 22 2018


STATUS

approved



