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 A202523 Number of partitions of n into distinct parts having pairwise prime GCDs but no overall common factor. 1
 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 4, 0, 0, 0, 1, 0, 4, 0, 1, 0, 5, 0, 4, 0, 0, 0, 3, 0, 5, 0, 0, 0, 6, 0, 1, 1, 2, 0, 6, 0, 6, 1, 1, 0, 4, 0, 12, 0, 1, 1, 12, 1, 9, 0, 0, 1, 10, 0, 10, 0, 1, 2, 10, 1, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 31,11 LINKS Alois P. Heinz, Table of n, a(n) for n = 31..251 EXAMPLE a(31) = 1: [6,10,15] = [2*3,2*5,3*5]. a(37) = 1: [10,12,15] = [2*5,2*2*3,3*5]. a(41) = 2: [6,15,20], [6,14,21]. a(43) = 1: [10,15,18]. a(47) = 1: [12,14,21]. a(49) = 1: [10,15,24]. a(61) = 4: [6,22,33], [10,15,36], [6,15,40], [6,10,45]. MAPLE w:=(m, h)-> mul(`if`(j[1]>=h, 1, j[1]^min(j[2], 2)), j=ifactors(m)[2]): b:= proc(n, i, g, s) option remember; local j, ok, si; if n=0 then `if`(g>1, 0, 1) elif i<2 or member(1, s) then 0 else ok:= evalb(i<=n); si:= map(x->w(x, i), s); for j in s while ok do ok:= isprime(igcd(i, j)) od; b(n, i-1, g, si) +`if`(ok, b(n-i, i-1, igcd(i, g), si union {w(i, i)} ), 0) fi end: a:= n-> b(n, n, 0, {}): seq(a(n), n=31..100); MATHEMATICA w[m_, h_] := Product[If[j[[1]] >= h, 1, j[[1]]^Min[j[[2]], 2]], {j, FactorInteger[m]}]; b[n_, i_, g_, s_] := b[n, i, g, s] = Module[{j, ok, si}, Which[n == 0, If[g > 1, 0, 1], i < 2 || MemberQ[s, 1], 0, True, ok = i <= n; si = w[#, i]& /@ s; For[j = 1, j <= Length[s], j++, If[!ok, Break[]]; ok = PrimeQ[ GCD[i, s[[j]]]]]; b[n, i - 1, g, si] + If[ok, b[n - i, i - 1, GCD[i, g], si ~Union~ {w[i, i]}], 0]]]; a[n_] := b[n, n, 0, {}]; Table[a[n], {n, 31, 100}] (* Jean-François Alcover, Dec 05 2020, after Alois P. Heinz *) CROSSREFS Cf. A202385, A202425, A200976, A018783. Sequence in context: A289618 A161520 A070097 * A215935 A270573 A096271 Adjacent sequences: A202520 A202521 A202522 * A202524 A202525 A202526 KEYWORD nonn AUTHOR Alois P. Heinz, Dec 20 2011 STATUS approved

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Last modified January 30 19:10 EST 2023. Contains 359947 sequences. (Running on oeis4.)