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!)
 A280226 Number of partitions of 2n into two squarefree parts. 11
 1, 2, 2, 3, 2, 4, 3, 5, 4, 6, 5, 7, 5, 7, 5, 8, 7, 11, 7, 11, 8, 13, 8, 13, 8, 14, 10, 13, 11, 15, 11, 15, 11, 18, 13, 21, 14, 20, 13, 20, 13, 22, 14, 23, 17, 23, 17, 24, 17, 25, 18, 26, 19, 31, 19, 29, 20, 31, 20, 31, 20, 33, 23, 30, 23, 32, 23, 32, 23, 35, 24, 41, 25, 39 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 FORMULA a(n) = Sum_{i=1..n} mu(i)^2 * mu(2n-i)^2, where mu is the Möbius function (A008683). EXAMPLE From Wesley Ivan Hurt, Feb 20 2018: (Start) a(5) = 2; there are two partitions of 2*5 = 10 into two squarefree parts: (7,3), (5,5). a(6) = 4; there are four partitions of 2*6 = 12 into two squarefree parts: (11,1), (10,2), (7,5), (6,6). a(7) = 3; there are three partitions of 2*7 = 14 into two squarefree parts: (13,1), (11,3), (7,7). a(8) = 5; there are five partitions of 2*8 = 16 into two squarefree parts: (15,1), (14,2), (13,3), (11,5), (10,6). (End) MAPLE with(numtheory): A280226:=n->sum(mobius(i)^2*mobius(2*n-i)^2, i=1..n): seq(A280226(n), n=1..100); MATHEMATICA f[n_] := Sum[(MoebiusMu[i]*MoebiusMu[2n -i])^2, {i, n}]; Array[f, 74] (* Robert G. Wilson v, Dec 29 2016 *) PROG (PARI) a(n)=sum(i=1, n, issquarefree(i) && issquarefree(2*n-i)) \\ Charles R Greathouse IV, Nov 05 2017 CROSSREFS Cf. A008683, A045917, A262991, A280250, A280251, A280252, A294248. Sequence in context: A322355 A242112 A211316 * A307995 A061889 A240089 Adjacent sequences:  A280223 A280224 A280225 * A280227 A280228 A280229 KEYWORD nonn,easy AUTHOR Wesley Ivan Hurt, Dec 29 2016 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 June 7 02:48 EDT 2020. Contains 334836 sequences. (Running on oeis4.)