A319527 a(n) = 7 * sigma(n).

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

Author

Omar E. Pol, Sep 22 2018

Keywords

• nonn
• easy

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).

Links

• Omar E. Pol, Diagram of the triangle A237593 before the (360/7)-degree-zig-zag folding (rows: 1..28)
• Index entries for sequences related to sigma(n)

Crossrefs

k times sigma(n), k=1..8: A000203, A074400, A272027, A239050, A274535, A274536, this sequence, A319528.

Cf. A216606, A237593.

Programs

GAP

List([1..70],n->7*Sigma(n)); # Muniru A Asiru, Sep 28 2018

Maple

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

Mathematica

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

PARI

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

Formula

a(n) = 7*A000203(n).

a(n) = A000203(n) + A274536(n).

Dirichlet g.f.: 7*zeta(s-1)*zeta(s). - (After Ilya Gutkovskiy)