

A319527


a(n) = 7 * sigma(n).


7



7, 21, 28, 49, 42, 84, 56, 105, 91, 126, 84, 196, 98, 168, 168, 217, 126, 273, 140, 294, 224, 252, 168, 420, 217, 294, 280, 392, 210, 504, 224, 441, 336, 378, 336, 637, 266, 420, 392, 630, 294, 672, 308, 588, 546, 504, 336, 868, 399, 651, 504, 686, 378, 840, 504, 840, 560, 630, 420, 1176, 434, 672, 728, 889
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OFFSET

1,1


COMMENTS

7 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 step pyramid (starting from the top) in which the structure of every (360/7)degreethreedimensional sector arises after the (360/7)degreezigzag folding of every row of the diagram of the isosceles triangle A237593. The top of the pyramid is a sevenpointed star formed by seven rhombuses (see Links section).


LINKS

Table of n, a(n) for n=1..64.
Omar E. Pol, Diagram of the triangle A237593 before the (360/7)degreezigzag folding (rows: 1..28)
Index entries for sequences related to sigma(n)


FORMULA

a(n) = 7*A000203(n).
a(n) = A000203(n) + A274536(n).
Dirichlet g.f.: 7*zeta(s1)*zeta(s).  (After Ilya Gutkovskiy)


MAPLE

with(numtheory): seq(7*sigma(n), n=1..64);


MATHEMATICA

7*DivisorSigma[1, Range[70]] (* Harvey P. Dale, Mar 14 2020 *)


PROG

(PARI) a(n) = 7 * sigma(n);
(GAP) List([1..70], n>7*Sigma(n)); # Muniru A Asiru, Sep 28 2018


CROSSREFS

k times sigma(n), k=1..8: A000203, A074400, A272027, A239050, A274535, A274536, this sequence, A319528.
Cf. A216606, A237593.
Sequence in context: A063469 A155131 A160890 * A297178 A325553 A032639
Adjacent sequences: A319524 A319525 A319526 * A319528 A319529 A319530


KEYWORD

nonn,easy


AUTHOR

Omar E. Pol, Sep 22 2018


STATUS

approved



