A370395 Numbers k that are neither squarefree nor prime powers sandwiched between twin primes.

12, 18, 60, 72, 108, 150, 180, 192, 198, 228, 240, 270, 312, 348, 420, 432, 522, 600, 660, 810, 828, 882, 1020, 1032, 1050, 1062, 1092, 1152, 1278, 1320, 1428, 1452, 1488, 1608, 1620, 1668, 1788, 1872, 1932, 1950, 1998, 2028, 2088, 2112, 2142, 2268, 2340, 2550

Offset: 1

Author

Michael De Vlieger, Mar 27 2024

Keywords

• nonn
• easy

Comments

Contains A113839 \ {4}.

This sequence contains 1062, 1278, 1608 while A258838 does not; A258838 includes 4, 6, 30, 42, 462, 570, etc.

Examples

			The number 12 is neither squarefree nor a prime power but comes between primes 11 and 13.
The number 30 is squarefree, though it comes between primes 29 and 31, it is not in the sequence.
		

Links

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

Crossrefs

Cf. A001359, A006512, A014574, A113839, A126706, A258838.

Programs

Mathematica

Select[1 + Select[Prime@ Range[100], PrimeQ[# + 2] &], Nor[SquareFreeQ[#], PrimePowerQ[#]] &]

Formula

Intersection of A014574 and A126706.