A339394 - OEIS

%I #10 Mar 09 2021 05:07:53

%S 0,1,3,6,15,26,43,81,138,218,320,514,751,1131,1570,2319,3159,4457,

%T 6077,8344,11224,15337,20297,26908,35773,46434,60711,78433,100987,

%U 129222,166590,209719,267120,335842,423341,527739,659974,816805,1015990,1251686,1543864

%N Sum over all partitions of n of the LCM of the number of parts and the number of distinct parts.

%H Alois P. Heinz, <a href="/A339394/b339394.txt">Table of n, a(n) for n = 0..1000</a>

%p b:= proc(n, i, p, d) option remember; `if`(n=0, ilcm(p, d),

%p       add(b(n-i*j, i-1, p+j, d+signum(j)), j=`if`(i>1, 0..n/i, n)))

%p     end:

%p a:= n-> b(n$2, 0$2):

%p seq(a(n), n=0..50);

%t b[n_, i_, p_, d_] := b[n, i, p, d] = If[n == 0, LCM[p, d],

%t      Sum[b[n - i*j, i - 1, p + j, d + Sign[j]],

%t      {j, If[i > 1, Range[0, n/i], {n}]}]];

%t a[n_] := b[n, n, 0, 0];

%t a /@ Range[0, 50] (* _Jean-François Alcover_, Mar 09 2021, after _Alois P. Heinz_ *)

%Y Cf. A003990, A051173, A339312.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Dec 02 2020