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 A294104 Sum of the differences of the larger and smaller parts in the partitions of n into two squarefree parts or two nonsquarefree parts. 1
 0, 0, 1, 2, 1, 4, 8, 12, 8, 4, 10, 24, 22, 20, 29, 54, 33, 40, 31, 72, 37, 70, 54, 114, 68, 62, 74, 116, 97, 62, 114, 182, 136, 126, 147, 292, 175, 134, 180, 330, 214, 182, 227, 412, 273, 190, 209, 460, 343, 202, 156, 468, 392, 380, 156, 518, 394, 490, 303 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 Index entries for sequences related to partitions FORMULA a(n) = Sum_{i=1..floor(n/2)} (n - 2i) * [A008966(i) = A008966(n-i)], where [] is the Iverson bracket. MAPLE f:= n -> add(n-2*i, i = select(t -> numtheory:-issqrfree(t)=numtheory:-issqrfree(n-t), [\$1..n/2])): map(f, [\$1..100]); # Robert Israel, Jun 12 2020 MATHEMATICA Table[Sum[(n - 2 k) KroneckerDelta[MoebiusMu[k]^2, MoebiusMu[ n - k]^2], {k, Floor[n/2]}], {n, 80}] CROSSREFS Cf. A008966, A294100. Sequence in context: A156817 A008301 A363386 * A294061 A113820 A319479 Adjacent sequences: A294101 A294102 A294103 * A294105 A294106 A294107 KEYWORD nonn,easy,look AUTHOR Wesley Ivan Hurt, Oct 22 2017 STATUS approved

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Last modified February 22 06:21 EST 2024. Contains 370240 sequences. (Running on oeis4.)