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 A087188 Number of partitions of n into distinct squarefree parts. 20
 1, 1, 1, 2, 1, 2, 3, 3, 4, 4, 5, 6, 6, 8, 9, 10, 13, 14, 16, 18, 20, 24, 27, 30, 35, 37, 42, 47, 51, 59, 64, 72, 81, 88, 98, 109, 120, 134, 147, 163, 179, 195, 216, 236, 258, 284, 310, 339, 371, 403, 441, 480, 523, 572, 621, 675, 734, 796, 865, 937, 1014, 1100, 1189 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..10000 FORMULA O.g.f.: product_{i=1,2,...infinity} [1+x^A005117(i)]. - R. J. Mathar, May 16 2008 a(n) ~ exp(sqrt(2*n)) / (2^(1/4) * sqrt(Pi) * n^(3/4)). - Vaclav Kotesovec, Mar 24 2018 EXAMPLE n=9: 5+3+1 = 6+2+1 = 6+3 = 7+2: a(9)=4; n=10: 5+3+2 = 6+3+1 = 7+2+1 = 7+3 = 10: a(10)=5. MAPLE with(numtheory): b:= proc(n, i) option remember; `if`(i*(i+1)/2 b(n\$2): seq(a(n), n=0..100); # Alois P. Heinz, Jun 02 2015 MATHEMATICA b[n_, i_] := b[n, i] = If[i*(i+1)/2 < n, 0, If[n == 0, 1, b[n, i-1] + If[i <= n && SquareFreeQ[i], b[n-i, i-1], 0]]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Jun 24 2015, after Alois P. Heinz *) nmax = 100; CoefficientList[Series[Exp[Sum[(-1)^(j + 1)/j * Sum[Abs[MoebiusMu[k]] * x^(j*k), {k, 1, Floor[nmax/j] + 1}], {j, 1, nmax}]], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 31 2018 *) PROG (Haskell) a087188 = p a005117_list where p _ 0 = 1 p (k:ks) m = if m < k then 0 else p ks (m - k) + p ks m -- Reinhard Zumkeller, Jun 01 2015 (PARI) ok(v)=for(i=2, #v, if(v[i]==v[i-1] || !issquarefree(v[i]), return(0))); #v==0 || issquarefree(v[1]) a(n)=my(s, u); forpart(v=n, if(ok(v), s++)); s \\ Charles R Greathouse IV, Nov 05 2017 CROSSREFS Cf. A073576, A000009, A005117, A008966, A225245, A256012. Sequence in context: A361165 A358024 A358025 * A102885 A323089 A239511 Adjacent sequences: A087185 A087186 A087187 * A087189 A087190 A087191 KEYWORD nonn AUTHOR Reinhard Zumkeller, Aug 24 2003 EXTENSIONS Offset changed and a(0)=1 prepended by Reinhard Zumkeller, Jun 01 2015 STATUS approved

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Last modified December 4 08:33 EST 2023. Contains 367558 sequences. (Running on oeis4.)