This site is supported by donations to The OEIS Foundation. Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A294283 Sum of the larger parts of the partitions of n into two distinct parts with smaller part squarefree. 0
 0, 0, 2, 3, 7, 9, 15, 18, 21, 24, 33, 37, 48, 53, 66, 72, 78, 84, 90, 96, 113, 120, 139, 147, 155, 163, 185, 194, 218, 228, 254, 265, 276, 287, 316, 328, 340, 352, 384, 397, 410, 423, 458, 472, 509, 524, 563, 579, 595, 611, 627, 643, 686, 703, 720, 737, 754 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Sum of the lengths of the distinct rectangles with squarefree width and positive integer length such that L + W = n, W < L. For example, a(14) = 53; the rectangles are 1 X 13, 2 X 12, 3 X 11, 5 X 9, 6 X 8. The sum of the lengths is then 13 + 12 + 11 + 9 + 8 = 53. - Wesley Ivan Hurt, Nov 12 2017 LINKS FORMULA a(n) = Sum_{i=1..floor((n-1)/2)} (n - i) * mu(i)^2, where mu is the Möbius function (A008683). EXAMPLE a(5) = 7; the partitions of 5 into two distinct parts are (4,1) and (3,2). The smaller parts are both squarefree, so the sum of the larger parts is 4+3 = 7. a(10) = 24; the partitions of 10 into two distinct parts are (9,1), (8,2), (7,3) and (6,4). Of the smaller parts, only 1, 2, and 3 are squarefree, so we add the larger parts of those partitions to get 9+8+7 = 24. MATHEMATICA Table[Sum[(n - i) MoebiusMu[i]^2, {i, Floor[(n-1)/2]}], {n, 60}] PROG (PARI) a(n) = sum(i=1, (n-1)\2, (n-i)*moebius(i)^2); \\ Michel Marcus, Nov 08 2017 CROSSREFS Cf. A008683, A008966, A262869, A262871, A294146. Sequence in context: A014837 A019312 A135369 * A294122 A211539 A109660 Adjacent sequences:  A294280 A294281 A294282 * A294284 A294285 A294286 KEYWORD nonn,easy AUTHOR Wesley Ivan Hurt, Oct 26 2017 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 December 10 15:09 EST 2019. Contains 329896 sequences. (Running on oeis4.)