login
A363814
Intersection of A126706 and A055932.
2
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
1,1
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).
LINKS
FORMULA
Union of A056808 and A364710. - Michael De Vlieger, Jan 31 2024
EXAMPLE
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.
MATHEMATICA
Select[Range[12, 1080, 2], And[AnyTrue[#2, # > 1 &], Length[#1] > 1, Union@ Differences@ PrimePi[#1] == {1}] & @@ Transpose@ FactorInteger[#] &]
KEYWORD
nonn,easy
AUTHOR
Michael De Vlieger, Dec 18 2023
STATUS
approved