A373559 Squares k such that rad(k) is a primorial number.

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

Author

David James Sycamore, Jun 09 2024

Keywords

• nonn
• easy

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)

Examples

			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).
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000290, A002110, A007947, A055932,

Programs

Mathematica

{1}~Join~Select[Range[2, 512, 2], Or[# == {2}, Union@ Differences@ PrimePi[#] == {1}] &@ FactorInteger[#][[All, 1]] &]^2 (* Michael De Vlieger, Jun 09 2024 *)

Formula

a(n) = A055932(n)^2.

Extensions

More terms from David A. Corneth, Jun 09 2024