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 A051424 Number of partitions of n into pairwise relatively prime parts. 58
 1, 1, 2, 3, 4, 6, 7, 10, 12, 15, 18, 23, 27, 33, 38, 43, 51, 60, 70, 81, 92, 102, 116, 134, 153, 171, 191, 211, 236, 266, 301, 335, 367, 399, 442, 485, 542, 598, 649, 704, 771, 849, 936, 1023, 1103, 1185, 1282, 1407, 1535, 1662, 1790, 1917, 2063, 2245, 2436 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..400 Eric Schmutz, Partitions whose parts are pairwise relatively prime, Discrete Math. 81(1) (1990), 87-89. Temba Shonhiwa, Compositions with pairwise relatively prime summands within a restricted setting, Fibonacci Quart. 44(4) (2006), 316-323. FORMULA log a(n) ~ (2*Pi/sqrt(6)) sqrt(n/log n). - Eric M. Schmidt, Jul 04 2013 Apparently no formula or recurrence is known. - N. J. A. Sloane, Mar 05 2017 EXAMPLE a(4) = 4 since all partitions of 4 consist of relatively prime numbers except 2+2. The a(6) = 7 partitions with pairwise coprime parts: (111111), (21111), (3111), (321), (411), (51), (6). - Gus Wiseman, Apr 14 2018 MAPLE with(numtheory): b:= proc(n, i, s) option remember; local f;       if n=0 or i=1 then 1     elif i<2 then 0     else f:= factorset(i);          b(n, i-1, select(x->is(xis(x b(n, n, {}): seq(a(n), n=0..80);  # Alois P. Heinz, Mar 14 2012 MATHEMATICA b[n_, i_, s_] := b[n, i, s] = Module[{f}, If[n == 0 || i == 1, 1, If[i < 2, 0, f = FactorInteger[i][[All, 1]]; b[n, i-1, Select[s, # < i &]] + If[i <= n && f ~Intersection~ s == {}, b[n-i, i-1, Select[s ~Union~ f, # < i &]], 0]]]]; a[n_] := b[n, n, {}]; Table[a[n], {n, 0, 54}] (* Jean-François Alcover, Oct 03 2013, translated from Maple, after Alois P. Heinz *) PROG (Haskell) a051424 = length . filter f . partitions where    f [] = True    f (p:ps) = (all (== 1) \$ map (gcd p) ps) && f ps    partitions n = ps 1 n where      ps x 0 = [[]]      ps x y = [t:ts | t <- [x..y], ts <- ps t (y - t)] -- Reinhard Zumkeller, Dec 16 2013 CROSSREFS Number of partitions of n into relatively prime parts = A000837. Row sums of A282749. Cf. A000837, A007359, A007360, A051424, A289509, A298748, A302569, A302696, A302797. Sequence in context: A163180 A091515 A036405 * A308632 A137606 A320224 Adjacent sequences:  A051421 A051422 A051423 * A051425 A051426 A051427 KEYWORD nonn AUTHOR EXTENSIONS More precise definition from Vladeta Jovovic, Dec 11 2004 STATUS approved

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Last modified July 9 16:50 EDT 2020. Contains 335545 sequences. (Running on oeis4.)