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A373559
Squares k such that rad(k) is a primorial number.
1
1, 4, 16, 36, 64, 144, 256, 324, 576, 900, 1024, 1296, 2304, 2916, 3600, 4096, 5184, 8100, 9216, 11664, 14400, 16384, 20736, 22500, 26244, 32400, 36864, 44100, 46656, 57600, 65536, 72900, 82944, 90000, 104976, 129600, 147456, 176400, 186624, 202500, 230400, 236196, 262144
OFFSET
1,2
COMMENTS
Squares k such that the squarefree kernel of k is primorial.
Intersection of A000290 and A055932.
1 is the only primorial term.
From Michael De Vlieger, Jun 09 2024: (Start)
Contains k^2 for k in each of A000079, A033845, A143207, A147571, A147572, etc.
Contains k^2 such that k is a product of primorials, i.e., A025487(i)^2, i >= 1, since A025487 is a proper subset of A055932.
(End)
LINKS
FORMULA
a(n) = A055932(n)^2.
EXAMPLE
1 is a square, rad(1) = 1 = A002110(0).
4 is a square and rad(4) = 2 = A002110(1).
36 is a square and rad(36) = 6 = A002110(2).
MATHEMATICA
{1}~Join~Select[Range[2, 512, 2], Or[# == {2}, Union@ Differences@ PrimePi[#] == {1}] &@ FactorInteger[#][[All, 1]] &]^2 (* Michael De Vlieger, Jun 09 2024 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from David A. Corneth, Jun 09 2024
STATUS
approved