The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A369889 The sum of squarefree divisors of the cubefree numbers. 1
 1, 3, 4, 3, 6, 12, 8, 4, 18, 12, 12, 14, 24, 24, 18, 12, 20, 18, 32, 36, 24, 6, 42, 24, 30, 72, 32, 48, 54, 48, 12, 38, 60, 56, 42, 96, 44, 36, 24, 72, 48, 8, 18, 72, 42, 54, 72, 80, 90, 60, 72, 62, 96, 32, 84, 144, 68, 54, 96, 144, 72, 74, 114, 24, 60, 96, 168 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The number of squarefree divisors of the n-th cubefree number is A366536(n). LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 FORMULA a(n) = A048250(A004709(n)). Sum_{j=1..n} a(j) ~ c * n^2, where c = zeta(3)^2/(2*zeta(5)) = 0.6967413068... . In general, the formula holds for the sum of squarefree divisors of the k-free numbers with c = zeta(k)^2/(2*zeta(2*k-1))..., for k >= 2. MATHEMATICA f[p_, e_] := p + 1; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; cubefreeQ[n_] := Max[FactorInteger[n][[;; , 2]]] < 3; s /@ Select[Range[100], cubefreeQ] (* or *) f[p_, e_] := If[e > 2, 0, p + 1]; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Array[s, 100], # > 0 &] PROG (PARI) lista(kmax) = {my(f, s, p, e); for(k = 1, kmax, f = factor(k); s = prod(i = 1, #f~, p = f[i, 1]; e = f[i, 2]; if(e < 3, p + 1, 0)); if(s > 0, print1(s, ", "))); } CROSSREFS Cf. A004709, A048250, A062822, A366440, A366536, A366537. Cf. A002117, A013663. Sequence in context: A340323 A046897 A109506 * A365481 A000113 A365347 Adjacent sequences: A369886 A369887 A369888 * A369890 A369891 A369892 KEYWORD nonn,easy AUTHOR Amiram Eldar, Feb 15 2024 STATUS approved

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

Last modified May 19 06:35 EDT 2024. Contains 372666 sequences. (Running on oeis4.)