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A331198 Numbers n with exactly three times as many factorizations (A001055) as strict factorizations (A045778). 0
128, 2187, 10368, 34992, 78125, 80000, 307328, 823543, 1250000, 1366875, 1874048, 3655808, 5250987, 6328125, 10690688, 13176688, 16681088, 19487171, 32019867, 35819648, 62462907, 62748517, 66706983, 90531968, 118210688, 182660427, 187578125, 239892608, 285012027 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Contains p^7 for all primes p.
LINKS
EXAMPLE
The 15 factorizations and 5 strict factorizations of 2187:
(2187) (2187)
(27*81) (27*81)
(3*729) (3*729)
(9*243) (9*243)
(3*9*81) (3*9*81)
(9*9*27)
(3*27*27)
(3*3*243)
(3*9*9*9)
(3*3*3*81)
(3*3*9*27)
(3*3*3*9*9)
(3*3*3*3*27)
(3*3*3*3*3*9)
(3*3*3*3*3*3*3)
MATHEMATICA
facsm[n_]:=facsm[n]=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facsm[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];
Select[Range[100000], 3==Length[facsm[#]]/Length[Select[facsm[#], UnsameQ@@#&]]&]
CROSSREFS
Factorizations are A001055.
Strict factorizations are A045778.
Taking "twice" instead of "three times" gives A001248.
Sequence in context: A351195 A223954 A224138 * A250365 A017678 A123253
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 12 2020
EXTENSIONS
a(7)-(10) from Alois P. Heinz, Jan 17 2020
a(11)-a(29) from Giovanni Resta, Jan 20 2020
STATUS
approved

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Last modified February 26 05:55 EST 2024. Contains 370335 sequences. (Running on oeis4.)