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 A294247 Sum of the parts in the partitions of n into exactly two distinct squarefree parts. 2
 0, 0, 3, 4, 5, 6, 14, 24, 18, 10, 22, 36, 39, 28, 45, 80, 68, 72, 57, 100, 84, 88, 92, 168, 125, 104, 135, 168, 145, 120, 155, 256, 198, 204, 210, 396, 259, 228, 273, 440, 328, 294, 387, 528, 450, 322, 376, 624, 490, 400, 357, 676, 530, 540, 385, 728, 570 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS One-half of the sum of the perimeters of the distinct rectangles with squarefree length and width such that L + W = n, W < L. LINKS FORMULA a(n) = n * Sum_{i=1..floor((n-1)/2)} mu(i)^2 * mu(n-i)^2, where mu(n) is the Möbius function (A008683). EXAMPLE For n = 4,5,6,7 the partitions are respectively 1+3 (sum a(4) = 4), 2+3 (sum 5), 1+5 (sum 6), 1+6 and 2+5, sum 7+7+14). - N. J. A. Sloane, Oct 28 2017 MATHEMATICA Table[n*Sum[MoebiusMu[i]^2*MoebiusMu[n - i]^2, {i, Floor[(n-1)/2]}], {n, 80}] PROG (Python) from sympy import mobius def a(n): return n*sum(mobius(i)**2*mobius(n - i)**2 for i in range(1, ((n - 1)//2) + 1)) print([a(n) for n in range(1, 51)]) # Indranil Ghosh, Nov 07 2017 (R) require(numbers) a <- function(n) {   if (n<3) return(0)   S <- numeric()   for (i in 1:floor((n-1)/2)) S <- c(S, moebius(i)^2*moebius(n-i)^2)   return(n*sum(S)) } sapply(1:100, a) # Indranil Ghosh, Nov 07 2017 CROSSREFS Cf. A008683, A262351. Sequence in context: A299496 A070981 A107228 * A083401 A281829 A083400 Adjacent sequences:  A294244 A294245 A294246 * A294248 A294249 A294250 KEYWORD nonn,easy AUTHOR Wesley Ivan Hurt, Oct 25 2017; recomputed Oct 26 2017 with thanks to Andrey Zabolotskiy STATUS approved

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Last modified November 24 22:57 EST 2020. Contains 338616 sequences. (Running on oeis4.)