OFFSET
1,1
COMMENTS
3 times the sum of the divisors of n.
From Omar E. Pol, Jul 04 2016: (Start)
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) where the structure of every 120-degree three-dimensional sector arises after the 120-degree zig-zag folding of every row of the diagram of the isosceles triangle A237593. The top of the pyramid is a hexagon formed by three rhombuses (see Links section).
More generally, if k >= 3 then k*sigma(n) is also the total number of horizontal rhombuses in the terraces of the n-th level of an irregular stepped pyramid where the structure of every 360/k three-dimensional sector arises after the 360/k-degree zig-zag folding of every row of the diagram of the isosceles triangle A237593. If k >= 5 the top of the pyramid is a k-pointed star formed by k rhombuses. (End)
LINKS
FORMULA
Dirichlet g.f.: 3*zeta(s-1)*zeta(s). - Ilya Gutkovskiy, Jul 04 2016
a(n) = A274536(n)/2. - Antti Karttunen, Nov 16 2017
From Omar E. Pol, Oct 02 2018: (Start)
Conjecture 1: a(n) = sigma(2*n) = A062731(n) iff n is odd.
And more generally:
Conjecture 2: If p is prime then (p + 1)*sigma(n) = sigma(p*n) iff n is not a multiple of p. (End)
The above claims easily follow from the fact that sigma is multiplicative function, thus if p does not divide n, then sigma(p*n) = sigma(p)*sigma(n). - Antti Karttunen, Nov 21 2019
MAPLE
with(numtheory): seq(3*sigma(n), n=1..64);
MATHEMATICA
Table[3 DivisorSigma[1, n], {n, 64}] (* Michael De Vlieger, Apr 19 2016 *)
PROG
(PARI) a(n) = 3 * sigma(n);
(Magma) [3*SumOfDivisors(n): n in [1..70]]; // Vincenzo Librandi, Jul 30 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Apr 18 2016
STATUS
approved