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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A071068 Number of ways to write n as a sum of two unordered squarefree numbers. 22
0, 1, 1, 2, 1, 2, 2, 3, 2, 2, 2, 4, 3, 3, 3, 5, 4, 4, 3, 6, 4, 5, 4, 7, 5, 5, 5, 7, 5, 5, 5, 8, 6, 7, 6, 11, 7, 7, 7, 11, 8, 8, 9, 13, 10, 8, 8, 13, 10, 8, 7, 14, 10, 10, 7, 13, 10, 11, 9, 15, 11, 11, 11, 15, 11, 11, 11, 18, 12, 13, 11, 21, 13, 14, 13, 20, 14, 13, 14, 20, 16, 13, 13, 22, 15 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

The natural density of the squarefree numbers is 6/Pi^2, so An < a(n) < Bn for all large enough n with A < 6/Pi^2 - 1/2 and B > 3/Pi^2. The Schnirelmann density of the squarefree numbers is 53/88 > 1/2, and so a(n) > 0 for all n > 1 (in fact, a(n+1) >= 9n/88). It follows from Theoreme 3 bis. in Cohen, Dress, & El Marraki along with finite checking up to 16089908 that 0.10792n < a(n) < 0.303967n for n > 36. (The lower bound holds for n > 1.) - Charles R Greathouse IV, Feb 02 2016

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

Henri Cohen, Francois Dress, and Mahomed El Marraki, Explicit estimates for summatory functions linked to the Möbius μ-function, Funct. Approx. Comment. Math. 37:1 (2007), pp. 51-63.

FORMULA

a(n) = sum(i=1..floor(n/2), abs(mu(i)*mu(n-i)) ). - Wesley Ivan Hurt, May 20 2013

EXAMPLE

12=1+11=2+10=5+7=6+6 hence a(12)=4.

MATHEMATICA

Table[Sum[Abs[MoebiusMu[i] MoebiusMu[n - i]], {i, 1, Floor[n/2]}], {n, 1, 85}] (* Indranil Ghosh, Mar 10 2017 *)

PROG

(PARI) a(n)=sum(i=1, n\2, issquarefree(i)&&issquarefree(n-i)) \\ Charles R Greathouse IV, May 21 2013

(PARI) list(lim)=my(n=lim\1); concat(0, ceil(Vec((Polrev(vector(n, k, issquarefree(k-1))) + O('x^(n+1)))^2)/2)) \\ Charles R Greathouse IV, May 21 2013

CROSSREFS

Cf. A005117, A098235.

Sequence in context: A033265 A096004 A193495 * A240872 A328806 A326370

Adjacent sequences:  A071065 A071066 A071067 * A071069 A071070 A071071

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, May 26 2002

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 3 05:55 EDT 2020. Contains 336197 sequences. (Running on oeis4.)