The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A049200 Euler totient function phi applied to the n-th squarefree number. 3
 1, 1, 2, 4, 2, 6, 4, 10, 12, 6, 8, 16, 18, 12, 10, 22, 12, 28, 8, 30, 20, 16, 24, 36, 18, 24, 40, 12, 42, 22, 46, 32, 52, 40, 36, 28, 58, 60, 30, 48, 20, 66, 44, 24, 70, 72, 36, 60, 24, 78, 40, 82, 64, 42, 56, 88, 72, 60, 46, 72, 96, 100, 32, 102, 48, 52, 106, 108, 40, 72 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 D. R. Ward, Some Series Involving Euler's Function, Journal of the London Mathematical Society, Vol. 1, No. 4 (1927), pp. 210-214. FORMULA a(n) = A000010(A005117(n)). {phi(x) ; abs(mu(x)) = 1}. a(n) = Product_{k = 1..A001221(n)} (A265668(n,k) + 1). - Reinhard Zumkeller, Dec 13 2015 Sum_{n>=1} 1/(A005117(n)*a(n)) = A082695. - Amiram Eldar, Oct 14 2020 Lim_{n->oo} Sum_{k=1..n} 1/a(k) - log(a(n)) = A083343 (Ward, 1927). - Amiram Eldar, Mar 05 2021 EXAMPLE The 12th squarefree number is 17 and phi(17) is 16, so a(12)=16. MAPLE map(numtheory:-phi, select(numtheory:-issqrfree, [\$1..1000])); # Robert Israel, Jul 12 2015 MATHEMATICA EulerPhi/@Select[Range[200], SquareFreeQ] (* Harvey P. Dale, Jan 13 2015 *) PROG (PARI) lista(nn) = {for(n=1, nn, if (issquarefree(n), print1(eulerphi(n), ", "))); } \\ Michel Marcus, Jul 12 2015 (MAGMA) [EulerPhi(n): n in [1..300] | IsSquarefree(n)]; // Vincenzo Librandi, Jul 13 2015 (Haskell) a049200 1 = 1 a049200 n = product \$ map (subtract 1) \$ a265668_row n -- Reinhard Zumkeller, Dec 13 2015 CROSSREFS Cf. A000010, A005117, A013929, A083343. Cf. A001221, A082695, A265668. Sequence in context: A322071 A176342 A340148 * A164701 A325965 A198540 Adjacent sequences:  A049197 A049198 A049199 * A049201 A049202 A049203 KEYWORD nonn,easy AUTHOR STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 21 14:32 EDT 2021. Contains 343154 sequences. (Running on oeis4.)