login
A279788
Twice partitioned numbers where the first partition is constant and the latter partitions are strict.
5
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
0,3
EXAMPLE
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)).
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}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 18 2016
STATUS
approved