%I #20 Apr 01 2021 01:43:19
%S 1,6,16,32,53,81,113,153,197,248,304,368,434,510,590,676,767,867,969,
%T 1081,1195,1317,1445,1581,1717,1864,2016,2174,2336,2508,2680,2864,
%U 3050,3244,3444,3650,3857,4077,4301,4531,4763,5007,5251,5507,5765
%N a(n) = 1 + 3*n*(n+1) - Sum_{k=1..n} d(k), where d(k) is the number of divisors of k.
%C 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.
%F a(n) = 1 + A028896(n) - A006218(n).
%e 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.
%t Table[1+3n(n+1)-Sum[DivisorSigma[0,k],{k,n}],{n,0,44}] (* _Stefano Spezia_, Feb 08 2021 *)
%o (PARI) a(n)=1+3*n*(n+1)-sum(k=1,n,n\k)
%o (Python)
%o from sympy import integer_nthroot
%o 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
%Y Cf. A000005, A006218, A028896.
%K nonn
%O 0,2
%A _Luc Rousseau_, Feb 08 2021