OFFSET
1,4
COMMENTS
EXAMPLE
The counted factorizations of n = 2, 4, 8, 12, 24, 36, 48:
(2) (4) (8) (12) (24) (36) (48)
(2*2) (2*4) (2*6) (3*8) (4*9) (6*8)
(2*2*2) (3*4) (4*6) (6*6) (2*24)
(2*2*3) (2*12) (2*18) (3*16)
(2*2*6) (3*12) (4*12)
(2*3*4) (2*2*9) (2*3*8)
(2*2*2*3) (2*3*6) (2*4*6)
(3*3*4) (3*4*4)
(2*2*3*3) (2*2*12)
(2*2*2*6)
(2*2*3*4)
(2*2*2*2*3)
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];
sqq[n_]:=Max@@Differences[primeMS[n]]<=1;
Table[Length[Select[facs[n], And@@sqq/@#&]], {n, 100}]
CROSSREFS
A000005 counts divisors.
A001055 counts factorizations.
A003963 multiplies together the prime indices.
A356226 lists the lengths of maximal gapless submultisets of prime indices:
- length: A287170
- minimum: A356227
- maximum: A356228
- bisected length: A356229
- standard composition: A356230
- Heinz number: A356231
- positions of first appearances: A356232
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 28 2022
STATUS
approved