A363814 Intersection of A126706 and A055932.

12, 18, 24, 36, 48, 54, 60, 72, 90, 96, 108, 120, 144, 150, 162, 180, 192, 216, 240, 270, 288, 300, 324, 360, 384, 420, 432, 450, 480, 486, 540, 576, 600, 630, 648, 720, 750, 768, 810, 840, 864, 900, 960, 972, 1050, 1080, 1152, 1200, 1260, 1296, 1350, 1440, 1458

Offset: 1

Author

Michael De Vlieger, Dec 18 2023

Keywords

• nonn
• easy

Comments

Products m*P(i) of primorials P(i) = A002110(i) such that rad(m) | P(i), i > 1, m > 1, where rad(m) = A007947(m).

Examples

			Sequence contains terms k > 1 in {6 * A003586} since all are divisible by P(2) = 6 and by no prime q that does not divide 6. Therefore 12, 18, 24, etc. are in the sequence.
Sequence does not contain k > 1 in {10 * A003592} since such k are divisible by 5 but not 3. Hence, 20, 40, etc. are not in this sequence.
Sequence does not contain k > 1 in {15 * A003593} since such k are odd. Hence, 45, 135, etc. are not in this sequence, etc.
		

Links

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

Crossrefs

Cf. A002110, A007947, A013929, A024619, A055932, A056808, A126706, A364710.

Cf. A003586, A003592, A003593.

Programs

Mathematica

Select[Range[12, 1080, 2], And[AnyTrue[#2, # > 1 &], Length[#1] > 1, Union@ Differences@ PrimePi[#1] == {1}] & @@ Transpose@ FactorInteger[#] &]

Formula

Union of A056808 and A364710. - Michael De Vlieger, Jan 31 2024