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A279788 Twice partitioned numbers where the first partition is constant and the latter partitions are strict.

%I A279788 #10 Dec 21 2016 18:55:52
%S A279788 1,1,2,3,4,4,10,6,12,17,21,13,57,19,49,87,86,39,240,55,279,330,235,
%T A279788 105,1141,386,491,1217,1461,257,4804,341,2968,4225,1958,5898,18961,
%U A279788 761,3782,15007,30572,1261,66245,1611,32523,106951,13122,2591,283013,81390,182873
%N A279788 Twice partitioned numbers where the first partition is constant and the latter partitions are strict.
%H A279788 Alois P. Heinz, <a href="/A279788/b279788.txt">Table of n, a(n) for n = 0..10000</a>
%H A279788 Gus Wiseman, <a href="/A063834/a063834.txt">Sequences enumerating triangles of integer partitions</a>
%e A279788 The a(6)=10 twice-partitions are:
%e A279788 ((6)), ((51)), ((42)), ((3)(3)), ((3)(21)), ((21)(3)),
%e A279788 ((321)), ((2)(2)(2)), ((21)(21)), ((1)(1)(1)(1)(1)(1)).
%p A279788 with(numtheory):
%p A279788 b:= proc(n) option remember; `if`(n=0, 1, add(add(
%p A279788       `if`(d::odd, d, 0), d=divisors(j))*b(n-j), j=1..n)/n)
%p A279788     end:
%p A279788 a:= proc(n) option remember; `if`(n=0, 1,
%p A279788       add(b(n/d)^d, d=divisors(n)))
%p A279788     end:
%p A279788 seq(a(n), n=0..70);  # _Alois P. Heinz_, Dec 20 2016
%t A279788 Table[DivisorSum[n,PartitionsQ[n/#]^#&],{n,20}]
%Y A279788 Cf. A000005, A000009, A018818, A063834, A279787.
%K A279788 nonn
%O A279788 0,3
%A A279788 _Gus Wiseman_, Dec 18 2016