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

1, 1, 2, 3, 4, 4, 10, 6, 12, 17, 21, 13, 57, 19, 49, 87, 86, 39, 240, 55, 279, 330, 235, 105, 1141, 386, 491, 1217, 1461, 257, 4804, 341, 2968, 4225, 1958, 5898, 18961, 761, 3782, 15007, 30572, 1261, 66245, 1611, 32523, 106951, 13122, 2591, 283013, 81390, 182873

Offset: 0

Author

Gus Wiseman, Dec 18 2016

Keywords

• nonn

Examples

			The a(6)=10 twice-partitions are:
((6)), ((51)), ((42)), ((3)(3)), ((3)(21)), ((21)(3)),
((321)), ((2)(2)(2)), ((21)(21)), ((1)(1)(1)(1)(1)(1)).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000
• Gus Wiseman, Sequences enumerating triangles of integer partitions

Crossrefs

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

Programs

Maple

with(numtheory):
b:= proc(n) option remember; `if`(n=0, 1, add(add(
      `if`(d::odd, d, 0), d=divisors(j))*b(n-j), j=1..n)/n)
    end:
a:= proc(n) option remember; `if`(n=0, 1,
      add(b(n/d)^d, d=divisors(n)))
    end:
seq(a(n), n=0..70);  # Alois P. Heinz, Dec 20 2016

Mathematica

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