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A284825 Number of partitions of n into 3 parts without common divisors such that every pair of them has common divisors. 4
1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 3, 0, 5, 0, 0, 0, 1, 0, 5, 0, 1, 0, 6, 0, 6, 0, 0, 0, 4, 0, 6, 0, 0, 0, 9, 0, 2, 1, 2, 0, 9, 0, 8, 1, 1, 0, 5, 0, 14, 0, 1, 0, 15, 0, 14, 0, 0, 1, 14, 0, 14, 0, 2, 0, 15, 0, 6, 1, 2, 1, 11, 0, 18, 1, 1, 0, 10, 0, 23 (list; graph; refs; listen; history; text; internal format)
OFFSET

31,11

LINKS

Alois P. Heinz, Table of n, a(n) for n = 31..10000

FORMULA

a(n) > 0 iff n in { A230035 }.

a(n) = 0 iff n in { A230034 }.

EXAMPLE

a(31) = 1: [6,10,15] = [2*3,2*5,3*5].

a(41) = 2: [6,14,21], [6,15,20].

MAPLE

a:= proc(n) option remember; add(add(`if`(igcd(i, j)>1

      and igcd(i, j, n-i-j)=1 and igcd(i, n-i-j)>1 and

      igcd(j, n-i-j)>1, 1, 0), j=i..(n-i)/2), i=2..n/3)

    end:

seq(a(n), n=31..137);

MATHEMATICA

a[n_] := a[n] = Sum[Sum[If[GCD[i, j] > 1 && GCD[i, j, n - i - j] == 1 && GCD[i, n - i - j] > 1 && GCD[j, n - i - j] > 1, 1, 0], {j, i, (n - i)/2} ], {i, 2, n/3}];

Table[a[n], {n, 31, 137}] (* Jean-Fran├žois Alcover, Jun 13 2018, from Maple *)

CROSSREFS

Cf. A082024, A230034, A230035.

Sequence in context: A182032 A265245 A110270 * A318875 A187143 A187144

Adjacent sequences:  A284822 A284823 A284824 * A284826 A284827 A284828

KEYWORD

nonn,look

AUTHOR

Alois P. Heinz, Apr 03 2017

STATUS

approved

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Last modified October 20 20:12 EDT 2019. Contains 328272 sequences. (Running on oeis4.)