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A368682
Products of primorials that are perfect powers but not prime powers.
2
36, 144, 216, 576, 900, 1296, 1728, 2304, 3600, 5184, 7776, 9216, 13824, 14400, 20736, 27000, 32400, 36864, 44100, 46656, 57600, 82944, 110592, 129600, 147456, 176400, 186624, 216000, 230400, 248832, 279936, 331776, 373248, 518400, 589824, 705600, 746496, 810000
OFFSET
1,1
COMMENTS
Intersection of A025487 and A131605.
Proper subset of A286708.
Contains A365308 (perfect powers of composite primorials) and A368508 (perfect powers of composite superprimorials).
These numbers are perfect powers of some smaller product of primorials.
LINKS
FORMULA
This sequence is { A368681 \ A000079 }.
EXAMPLE
b(n) = A025487(n).
a(1) = b(11) = 36 = 6^2 = b(4)^2,
a(2) = b(19) = 144 = 12^2 = b(6)^2,
a(3) = b(23) = 216 = 6^3 = b(4)^3,
a(4) = b(33) = 576 = 24^2 = b(8)^2,
a(5) = b(38) = 900 = 30^2 = b(9)^2, etc.
MATHEMATICA
Select[Range[36, 2^18, 2], And[Union@ Differences@ PrimePi@ #1 == {1}, AllTrue[Union@ Differences@ #2, # <= 0 &], GCD @@ #2 > 1] & @@ Transpose@ FactorInteger[#] &]
KEYWORD
nonn
AUTHOR
Michael De Vlieger, Jan 02 2024
STATUS
approved