|
| |
|
|
A274536
|
|
a(n) = 6 * sigma(n).
|
|
11
|
|
|
|
6, 18, 24, 42, 36, 72, 48, 90, 78, 108, 72, 168, 84, 144, 144, 186, 108, 234, 120, 252, 192, 216, 144, 360, 186, 252, 240, 336, 180, 432, 192, 378, 288, 324, 288, 546, 228, 360, 336, 540, 252, 576, 264, 504, 468, 432, 288, 744, 342, 558, 432, 588, 324, 720, 432, 720, 480, 540, 360, 1008, 372, 576, 624, 762
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
6 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 60-degree-three-dimensional sector arises after the 60-degree-zig-zag folding of every row of the diagram of the isosceles triangle A237593. The top of the pyramid is a six-pointed star formed by six rhombuses (see Links section).
|
|
|
LINKS
|
Antti Karttunen, Table of n, a(n) for n = 1..10000
Omar E. Pol, Diagram of the triangle before the 60-degree-zig-zag folding (rows: 1..28)
Index entries for sequences related to sigma(n)
|
|
|
FORMULA
|
a(n) = 6*A000203(n) = 3*A074400(n) = 2*A272027(n).
a(n) = A000203(n) + A274535(n) = A074400(n) + A239050(n).
Dirichlet g.f.: 6*zeta(s-1)*zeta(s). - Ilya Gutkovskiy, Jul 04 2016
Conjecture: a(n) = sigma(5*n) = A283118(n) iff n is not a multiple of 5. - Omar E. Pol, Oct 02 2018
|
|
|
MAPLE
|
with(numtheory): seq(6*sigma(n), n=1..64);
|
|
|
MATHEMATICA
|
6DivisorSigma[1, Range[50]] (* Alonso del Arte, Jul 04 2016 *)
|
|
|
PROG
|
(PARI) a(n) = 6 * sigma(n);
|
|
|
CROSSREFS
|
k times sigma(n), k=1..8: A000203, A074400, A272027, A239050, A274535, this sequence, A319527, A319528.
Cf. A237593, A283118.
Sequence in context: A101527 A028887 A283118 * A051395 A256266 A228104
Adjacent sequences: A274533 A274534 A274535 * A274537 A274538 A274539
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
Omar E. Pol, Jun 29 2016
|
|
|
STATUS
|
approved
|
| |
|
|
