A357859 -id:A357859 - cp's OEIS frontend

A357860 Number of integer factorizations of n into distinct even factors.

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

Gus Wiseman, Oct 17 2022

nonn

			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

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.
Cf. A000009, A000688, A000961, A023894, A295935, A318721, A340785.

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}]

cp's OEIS Frontend

A357860 Number of integer factorizations of n into distinct even factors.

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