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 A000114 Number of cusps of principal congruence subgroup GAMMA^{hat}(n). 2
 3, 4, 6, 12, 12, 24, 24, 36, 36, 60, 48, 84, 72, 96, 96, 144, 108, 180, 144, 192, 180, 264, 192, 300, 252, 324, 288, 420, 288, 480, 384, 480, 432, 576, 432, 684, 540, 672, 576, 840, 576, 924, 720, 864, 792, 1104, 768, 1176, 900, 1152, 1008, 1404, 972, 1440 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS A001766(n) = n*a(n). - Michael Somos, Jan 29 2004 REFERENCES R. A. Rankin, Modular Forms and Functions, Cambridge 1977, p. 62. LINKS N. J. A. Sloane, Table of n, a(n) for n = 2..10000 Ioannis Ivrissimtzis, David Singerman, James Strudwick, From Farey fractions to the Klein quartic and beyond, arXiv:1909.08568 [math.GR], 2019. See mu(n)/n p. 3. A. Papoulis, A new method of inversion of the Laplace transform, Quart. Appl. Math 14 (1957), 405-414. [Annotated scan of selected pages] FORMULA a(n) = ((n^2)/2)*Product_{p | n, p prime} (1-1/p^2), for n>=3. - Michel Marcus, Oct 23 2019 MAPLE A000114 := proc(n) local b, d: if n = 2 then RETURN(3); else b := n^2/2; for d from 1 to n do if irem(n, d) = 0 and isprime(d) then b := b*(1-d^(-2)); fi; od; RETURN(b); fi: end: MATHEMATICA a[n_] := If[n == 2, 3, b = n^2/2; For[d = 1, d <= n, d++, If[Mod[n, d] == 0 && PrimeQ[d], b = b*(1-d^-2)]]; b]; Table[a[n], {n, 2, 50}] (* Jean-François Alcover, Feb 04 2016, adapted from Maple *) PROG (PARI) a(n) = if (n==2, 3, my(f=factor(n)); prod(k=1, #f~, 1-1/f[k, 1]^2)*n^2/2); \\ Michel Marcus, Oct 23 2019 CROSSREFS Cf. A001766. Sequence in context: A175894 A175029 A113728 * A310006 A294144 A136243 Adjacent sequences: A000111 A000112 A000113 * A000115 A000116 A000117 KEYWORD nonn,easy AUTHOR N. J. A. Sloane STATUS approved

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Last modified October 4 08:18 EDT 2023. Contains 365873 sequences. (Running on oeis4.)