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A202385 Number of partitions of n into distinct parts having pairwise common factors but no overall common factor. 3
1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 1, 0, 4, 0, 3, 0, 1, 0, 5, 0, 8, 0, 2, 0, 5, 0, 10, 0, 4, 0, 13, 0, 15, 0, 3, 1, 13, 0, 19, 0, 9, 1, 24, 0, 20, 2, 13, 2, 29, 0, 34, 2, 17, 2, 34, 1, 49, 2, 21, 3, 58, 2, 63, 3, 20, 7, 72, 2, 81, 3 (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) = 2: [6,10,12,15], [10,15,18].

a(53) = 4: [6,12,15,20], [15,18,20], [6,12,14,21], [14,18,21].

a(55) = 3: [10,12,15,18], [6,10,15,24], [6,21,28].

MAPLE

with(numtheory):

w:= (m, h)-> mul(`if`(j>=h, 1, j), j=factorset(m)):

b:= proc(n, i, g, s) option remember; local j, ok;

      if n<0 then 0

    elif n=0 then `if`(g>1, 0, 1)

    elif i<2 then 0

    else ok:= evalb(i<=n);

         for j in s while ok do ok:= igcd(i, j)>1 od;

         b(n, i-1, g, map(x->w(x, i), s)) +`if`(ok,

         b(n-i, i-1, igcd(i, g), map(x->w(x, i), {s[], i}) ), 0)

      fi

    end:

a:= n-> b(n, n, 0, {}):

seq(a(n), n=31..100);

MATHEMATICA

w[m_, h_] := Product[If[j >= h, 1, j], {j, FactorInteger[m][[All, 1]]}]; b[n_, i_, g_, s_] := b[n, i, g, s] = Module[{j, ok}, Which[n<0, 0, n==0, If[g>1, 0, 1], i<2, 0, True, ok = i <= n; For[j = 1, ok && j <= Length[s], j++, ok = GCD[i, s[[j]]]>1]; b[n, i-1, g, Map[w[#, i]&, s]] + If[ok, b[n-i, i-1, GCD[i, g], Map[w[#, i]&, Union @ Append[s, i]]], 0]]]; a[n_] := b[n, n, 0, {}]; Table[a[n], {n, 31, 100}] (* Jean-Fran├žois Alcover, Feb 15 2017, translated from Maple *)

CROSSREFS

Cf. A200976, A018783.

Sequence in context: A290542 A029834 A318715 * A029833 A050948 A282695

Adjacent sequences:  A202382 A202383 A202384 * A202386 A202387 A202388

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Dec 18 2011

STATUS

approved

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Last modified May 31 13:01 EDT 2020. Contains 334748 sequences. (Running on oeis4.)