|
|
A340785
|
|
Number of factorizations of 2n into even factors > 1.
|
|
15
|
|
|
1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 4, 1, 2, 1, 7, 1, 3, 1, 4, 1, 2, 1, 7, 1, 2, 1, 4, 1, 3, 1, 11, 1, 2, 1, 6, 1, 2, 1, 7, 1, 3, 1, 4, 1, 2, 1, 12, 1, 3, 1, 4, 1, 3, 1, 7, 1, 2, 1, 7, 1, 2, 1, 15, 1, 3, 1, 4, 1, 3, 1, 12, 1, 2, 1, 4, 1, 3, 1, 12, 1, 2, 1, 7, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
The a(n) factorizations for n = 2*2, 2*4, 2*8, 2*12, 2*16, 2*32, 2*36, 2*48 are:
4 8 16 24 32 64 72 96
2*2 2*4 2*8 4*6 4*8 8*8 2*36 2*48
2*2*2 4*4 2*12 2*16 2*32 4*18 4*24
2*2*4 2*2*6 2*2*8 4*16 6*12 6*16
2*2*2*2 2*4*4 2*4*8 2*6*6 8*12
2*2*2*4 4*4*4 2*2*18 2*6*8
2*2*2*2*2 2*2*16 4*4*6
2*2*2*8 2*2*24
2*2*4*4 2*4*12
2*2*2*2*4 2*2*4*6
2*2*2*2*2*2 2*2*2*12
2*2*2*2*6
|
|
MATHEMATICA
|
facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];
Table[Length[Select[facs[n], Select[#, OddQ]=={}&]], {n, 2, 100, 2}]
|
|
PROG
|
(PARI)
A349906(n, m=n) = if(1==n, 1, my(s=0); fordiv(n, d, if((d>1)&&(d<=m)&&!(d%2), s += A349906(n/d, d))); (s));
|
|
CROSSREFS
|
Note: A-numbers of Heinz-number sequences are in parentheses below.
- Factorizations -
A340653 counts balanced factorizations.
A316439 counts factorizations by product and length
A340102 counts odd-length factorizations of odd numbers into odd factors.
- Even -
A236913 counts partitions of even length and sum.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|