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 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
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified August 10 02:46 EDT 2024. Contains 375044 sequences. (Running on oeis4.)