OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..2500 (first 101 terms from Chai Wah Wu)
EXAMPLE
The a(1) = 1 through a(9) = 6 integer partitions:
1 2 3 4 5 6 7 8 9
11 111 22 32 33 52 44 72
1111 11111 222 322 53 333
111111 1111111 332 522
2222 3222
11111111 111111111
MAPLE
b:= proc(n, i, f) option remember; `if`(n=0, 1, `if`(i<1, 0,
b(n, i-1, f)+(o-> `if`(f in {0, o}, b(n-i, min(i, n-i),
`if`(f=0, o, f)), 0))(numtheory[bigomega](i))))
end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..75); # Alois P. Heinz, Dec 15 2018
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], SameQ@@PrimeOmega/@#&]], {n, 30}]
(* Second program: *)
b[n_, i_, f_] := b[n, i, f] = If[n == 0, 1, If[i < 1, 0,
b[n, i-1, f] + Function[o, If[f == 0 || f == o, b[n-i, Min[i, n-i],
If[f == 0, o, f]], 0]][PrimeOmega[i]]]];
a[n_] := b[n, n, 0];
a /@ Range[0, 75] (* Jean-François Alcover, May 10 2021, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 10 2018
EXTENSIONS
a(51)-a(58) from Chai Wah Wu, Nov 12 2018
STATUS
approved