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

1,8

Links

Table of n, a(n) for n=1..87.

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.

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

Sequence in context: A070105 A111397 A131743 * A147648 A363879 A366767

Adjacent sequences: A357857 A357858 A357859 * A357861 A357862 A357863

Keyword

nonn

Author

Gus Wiseman, Oct 17 2022

Status

approved