A279788 - OEIS

%I #10 Dec 21 2016 18:55:52

%S 1,1,2,3,4,4,10,6,12,17,21,13,57,19,49,87,86,39,240,55,279,330,235,

%T 105,1141,386,491,1217,1461,257,4804,341,2968,4225,1958,5898,18961,

%U 761,3782,15007,30572,1261,66245,1611,32523,106951,13122,2591,283013,81390,182873

%N Twice partitioned numbers where the first partition is constant and the latter partitions are strict.

%H Alois P. Heinz, <a href="/A279788/b279788.txt">Table of n, a(n) for n = 0..10000</a>

%H Gus Wiseman, <a href="/A063834/a063834.txt">Sequences enumerating triangles of integer partitions</a>

%e The a(6)=10 twice-partitions are:

%e ((6)), ((51)), ((42)), ((3)(3)), ((3)(21)), ((21)(3)),

%e ((321)), ((2)(2)(2)), ((21)(21)), ((1)(1)(1)(1)(1)(1)).

%p with(numtheory):

%p b:= proc(n) option remember; `if`(n=0, 1, add(add(

%p       `if`(d::odd, d, 0), d=divisors(j))*b(n-j), j=1..n)/n)

%p     end:

%p a:= proc(n) option remember; `if`(n=0, 1,

%p       add(b(n/d)^d, d=divisors(n)))

%p     end:

%p seq(a(n), n=0..70);  # _Alois P. Heinz_, Dec 20 2016

%t Table[DivisorSum[n,PartitionsQ[n/#]^#&],{n,20}]

%Y Cf. A000005, A000009, A018818, A063834, A279787.

%K nonn

%O 0,3

%A _Gus Wiseman_, Dec 18 2016