A341276 a(n) = 1 + 3*n*(n+1) - Sum_{k=1..n} d(k), where d(k) is the number of divisors of k.

1, 6, 16, 32, 53, 81, 113, 153, 197, 248, 304, 368, 434, 510, 590, 676, 767, 867, 969, 1081, 1195, 1317, 1445, 1581, 1717, 1864, 2016, 2174, 2336, 2508, 2680, 2864, 3050, 3244, 3444, 3650, 3857, 4077, 4301, 4531, 4763, 5007, 5251, 5507, 5765

Offset

0,2

Comments

Number of regions of the plane delimited by the 3n curves: x=k, y=k, x*y=k for k=1..n with x>0 and y>0.

Links

Table of n, a(n) for n=0..44.

Formula

a(n) = 1 + A028896(n) - A006218(n).

Example

The curves with equations x=1, y=1 and x*y=1 are delimiting a(1)=6 regions in the (+; +) quadrant of the plane. With the addition of the curves with equations x=2, y=2 and x*y=2, the number of delimited regions reaches a(2)=16.

Mathematica

Table[1+3n(n+1)-Sum[DivisorSigma[0, k], {k, n}], {n, 0, 44}] (* Stefano Spezia, Feb 08 2021 *)

Prog

(PARI) a(n)=1+3*n*(n+1)-sum(k=1, n, n\k)
(Python)
from sympy import integer_nthroot
def A341276(n): return 1+3*n*(n+1)-2*sum(n//k for k in range(1, integer_nthroot(n, 2)[0]+1))+integer_nthroot(n, 2)[0]**2 # Chai Wah Wu, Mar 31 2021

Crossrefs

Cf. A000005, A006218, A028896.

Sequence in context: A097118 A369548 A296957 * A301698 A301713 A134465

Adjacent sequences: A341273 A341274 A341275 * A341277 A341278 A341279

Keyword

nonn

Author

Luc Rousseau, Feb 08 2021

Status

approved