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A357860
Number of integer factorizations of n into distinct even factors.
1
1, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 2, 0, 1, 0, 2, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 5, 0, 1, 0, 3, 0, 1, 0
OFFSET
1,8
EXAMPLE
The factorizations of 36..48 are (empty columns indicated by dots):
36 . 38 . 40 . 42 . 44 . 46 . 48
2*18 2*20 2*22 6*8
4*10 2*24
4*12
2*4*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], UnsameQ@@#&&OddQ[Times@@(#+1)]&]], {n, 100}]
CROSSREFS
The non-strict version is A349906.
Same as A357859 with zeros every other term.
A000005 counts divisors.
A001055 counts factorizations.
A001221 counts distinct prime factors, sum A001414.
A001222 counts prime-power divisors.
A050361 counts strict factorizations into prime powers.
Sequence in context: A070105 A111397 A131743 * A147648 A363879 A366767
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 17 2022
STATUS
approved