|
|
A343014
|
|
Number with a record number of divisors whose prime factorizations contain no repeated exponents.
|
|
1
|
|
|
1, 2, 4, 8, 12, 24, 48, 72, 96, 144, 288, 432, 576, 720, 864, 1152, 1440, 2160, 2880, 4320, 5760, 8640, 12960, 17280, 25920, 34560, 43200, 51840, 69120, 77760, 86400, 103680, 129600, 155520, 172800, 207360, 259200, 345600, 388800, 518400, 777600, 907200, 1036800
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Since A181796(n) depends only on the prime signature of n, this sequence is a subsequence of A025487.
The corresponding record values are 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 16, 17, 19, 20, 21, 22, ... (see the link for more values).
Let G_m be the gcd of terms k with omega(k) = m. So G_1 <= 2, G_2 <= 12, G_3 <= 720, G_4 <= 907200.
Do we have G_m | G_(m + 1)? (End)
|
|
LINKS
|
|
|
EXAMPLE
|
A181796 begins with 1, 2, 2, 3, 2, 3, 2, 4, .... The record values, 1, 2, 3 and 4 occur at 1, 2, 4 and 8, which are the first 4 terms of this sequence.
|
|
MATHEMATICA
|
q[n_] := UnsameQ @@ FactorInteger[n][[;; , 2]]; s[n_] := DivisorSum[n, 1 &, q[#] &]; sm = 0; seq = {}; Do[s1 = s[n]; If[s1 > sm, sm = s1; AppendTo[seq, n]], {n, 1, 10^4}]; seq
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|