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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved