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A319527
a(n) = 7 * sigma(n).
11
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
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 n-th level of an irregular stepped pyramid (starting from the top) in which the structure of every (360/7)-degree-three-dimensional sector arises after the (360/7)-degree-zig-zag folding of every row of the diagram of the isosceles triangle A237593. The top of the pyramid is a seven-pointed star formed by seven rhombuses (see Links section).
FORMULA
a(n) = 7*A000203(n).
a(n) = A000203(n) + A274536(n).
Dirichlet g.f.: 7*zeta(s-1)*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.
Sequence in context: A063469 A155131 A160890 * A297178 A325553 A032639
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Sep 22 2018
STATUS
approved