A200792 - OEIS

%I #13 Feb 06 2017 08:45:49

%S 0,0,1,1,3,3,7,8,12,14,24,29,43,53,72,87,119,145,196,241,314,386,505,

%T 617,786,960,1202,1456,1813,2186,2698,3253,3975,4778,5827,6979,8463,

%U 10127,12217,14566,17509,20810,24895,29513,35128,41496,49220,57949,68445

%N Number of partitions of n such that the number of parts and the greatest part are not coprime.

%H Alois P. Heinz, <a href="/A200792/b200792.txt">Table of n, a(n) for n = 1..500</a>

%e a(5) = 3: [1,1,1,2], [1,1,3], [1,4].

%e a(6) = 3: [1,1,2,2], [1,2,3], [2,4].

%e a(7) = 7: [1,1,1,1,1,2], [1,2,2,2], [2,2,3], [1,3,3], [1,1,1,4], [3,4], [1,6].

%p b:= proc(n, j, t) option remember;

%p       add(b(n-i, i, t+1), i=j..iquo(n, 2))+

%p       `if`(igcd(t, n)>1, 1, 0)

%p     end:

%p a:= n-> b(n, 1, 1):

%p seq(a(n), n=1..60);

%t b[n_, j_, t_] := b[n, j, t] = Sum[b[n-i, i, t+1], {i, j, Quotient[n, 2]}] + If[GCD[t, n] > 1, 1, 0]; a[n_] := b[n, 1, 1]; Table[a[n], {n, 1, 60}] (* _Jean-François Alcover_, Feb 06 2017, translated from Maple *)

%Y Cf. A199887.

%K nonn

%O 1,5

%A _Alois P. Heinz_, Nov 22 2011