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Numbers k that are neither squarefree nor prime powers sandwiched between twin primes.
1

%I #21 Apr 04 2024 10:02:07

%S 12,18,60,72,108,150,180,192,198,228,240,270,312,348,420,432,522,600,

%T 660,810,828,882,1020,1032,1050,1062,1092,1152,1278,1320,1428,1452,

%U 1488,1608,1620,1668,1788,1872,1932,1950,1998,2028,2088,2112,2142,2268,2340,2550

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

%C Contains A113839 \ {4}.

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

%H Michael De Vlieger, <a href="/A370395/b370395.txt">Table of n, a(n) for n = 1..10000</a>

%F Intersection of A014574 and A126706.

%e The number 12 is neither squarefree nor a prime power but comes between primes 11 and 13.

%e The number 30 is squarefree, though it comes between primes 29 and 31, it is not in the sequence.

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

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

%K nonn,easy

%O 1,1

%A _Michael De Vlieger_, Mar 27 2024