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!)
 A294094 Sum of the differences of the larger and smaller parts in the partitions of 2n into two parts with the larger part prime and smaller part squarefree. 1
 0, 2, 4, 8, 4, 12, 20, 16, 28, 38, 28, 48, 32, 24, 56, 64, 68, 60, 68, 58, 112, 144, 104, 168, 124, 110, 180, 124, 152, 202, 192, 224, 204, 190, 188, 288, 344, 288, 300, 300, 304, 398, 344, 290, 464, 326, 384, 360, 304, 418, 540, 556, 444, 616, 608, 626, 764 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Sum of the slopes of the tangent lines along the left side of the parabola b(x) = 2*n*x-x^2 at squarefree values of x such that 2n-x is prime for x in 0 < x <= n. For example, d/dx 2*n*x-x^2 = 2n-2x. So for a(6), the squarefree values of x that make 12-x prime are x=1,5 and so a(6) = 12-2*1 + 12-2*5 = 10 + 2 = 12. - Wesley Ivan Hurt, Mar 25 2018 LINKS FORMULA a(n) = 2 * Sum_{i=1..n} (n - i) * A010051(2n - i) * A008966(i). EXAMPLE For n = 7, 14 can be partitioned into a prime and a smaller squarefree number in two ways: 13 + 1 and 11 + 3, so a(7) = (13 - 1) + (11 - 3) = 20. - Michael B. Porter, Mar 27 2018 MATHEMATICA Table[2*Sum[(n - i) (PrimePi[2 n - i] - PrimePi[2 n - i - 1]) MoebiusMu[i]^2, {i, n}], {n, 80}] PROG (PARI) a(n) = 2 * sum(i=1, n, (n-i)*isprime(2*n-i)*issquarefree(i)); \\ Michel Marcus, Mar 26 2018 CROSSREFS Cf. A010051, A008966, A294093. Sequence in context: A151569 A016635 A133992 * A290288 A126215 A165617 Adjacent sequences:  A294091 A294092 A294093 * A294095 A294096 A294097 KEYWORD nonn,easy AUTHOR Wesley Ivan Hurt, Oct 22 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 April 12 11:25 EDT 2021. Contains 342920 sequences. (Running on oeis4.)