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 A201218 Number of partitions of n such that the number of parts and the largest part and the smallest part are pairwise coprime. 2
 1, 1, 1, 3, 2, 5, 6, 12, 13, 22, 25, 40, 47, 69, 85, 126, 148, 204, 249, 330, 404, 531, 647, 835, 1022, 1300, 1591, 2006, 2432, 3029, 3678, 4541, 5477, 6711, 8056, 9805, 11735, 14178, 16918, 20356, 24195, 28963, 34372, 40978, 48486, 57626, 68001, 80540, 94826 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..300 EXAMPLE a(4) = 3: [1,1,1,1], [1,1,2], [1,3]; a(5) = 2: [1,1,1,1,1], [1,2,2]; a(6) = 5: [1,1,1,1,1,1], [1,1,1,1,2], [1,1,1,3], [1,1,4], [1,5]; a(7) = 6: [1,1,1,1,1,1,1], [1,1,1,2,2], [1,1,1,1,3], [1,1,2,3], [1,2,4], [1,1,5]; a(8) = 12: [1,1,1,1,1,1,1,1], [1,1,1,1,1,1,2], [1,1,2,2,2], [1,1,1,2,3], [1,2,2,3], [1,1,3,3], [1,1,1,1,4], [1,3,4], [1,1,1,5], [1,2,5], [3,5], [1,7]. MAPLE b:= proc(n, j, t, s) option remember; add(b(n-i, i, t+1, s), i=j..iquo(n, 2))+ `if`(igcd(t, s)=1 and igcd(t, n)=1 and igcd(n, s)=1, 1, 0) end: a:= n-> `if`(n=1, 1, add(b(n-i, i, 2, i), i=1..iquo(n, 2))): seq(a(n), n=1..60); MATHEMATICA b[n_, j_, t_, s_] := b[n, j, t, s] = Sum[b[n-i, i, t+1, s], {i, j, Quotient[n, 2]}] + If[GCD[t, s] == 1 && GCD[t, n] == 1 && GCD[n, s] == 1, 1, 0]; a[n_] := If[n == 1, 1, Sum [b[n-i, i, 2, i], {i, 1, Quotient[n, 2]}]]; Table[a[n], {n, 1, 60}] (* Jean-François Alcover, Oct 07 2014, translated from Maple *) CROSSREFS Cf. A199890. Sequence in context: A240574 A050061 A058638 * A139140 A047074 A303766 Adjacent sequences: A201215 A201216 A201217 * A201219 A201220 A201221 KEYWORD nonn AUTHOR Alois P. Heinz, Nov 28 2011 STATUS approved

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Last modified November 29 06:17 EST 2023. Contains 367422 sequences. (Running on oeis4.)