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 A280469 Numbers n such that n-1 and n+1 are squarefree and have the same number of prime factors. 2
 4, 6, 12, 18, 30, 34, 42, 56, 60, 72, 86, 92, 94, 102, 108, 138, 142, 144, 150, 160, 180, 184, 186, 192, 198, 202, 204, 214, 216, 218, 220, 228, 236, 240, 248, 266, 270, 282, 300, 302, 304, 312, 320, 322, 328, 340, 348, 392, 394, 412, 414, 416, 420, 432, 446 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS For a given term n of this sequence, n-1 and n+1 are both squarefree k-almost primes for the same k. The sequence is thus the union of the averages (arithmetic means) of twin prime pairs (A014574), the averages of twin squarefree semiprime pairs, the averages of twin squarefree 3-almost prime pairs, ... (where "twin ... pairs" means the members of each pair differ by two). A subsequence of A280382 and of A280383. LINKS Rick L. Shepherd, Table of n, a(n) for n = 1..10000 EXAMPLE The number 34 is a term because 33 = 3*11 and 35 = 5*7, a twin semiprime pair. Unlike A280382 and A280383, 19 is not a term here because 18 = 2*3^2 and 20  = 2^2*5, neither of which is squarefree. MATHEMATICA Select[Range@ 500, And[Times @@ First@ # == 1, SameQ @@ Last@ #] &@ Transpose@ Map[{Boole@ SquareFreeQ@ #, PrimeNu@ #} &, # + {-1, 1}] &] (* Michael De Vlieger, Jan 30 2017 *) PROG (PARI) IsInA280469(n) = n > 1 && issquarefree(n-1) && issquarefree(n+1) && omega(n-1) == omega(n+1) CROSSREFS Cf. A014574, A280382, A280383. Sequence in context: A068570 A074998 A061715 * A072570 A217259 A014574 Adjacent sequences:  A280466 A280467 A280468 * A280470 A280471 A280472 KEYWORD nonn AUTHOR Rick L. Shepherd, Jan 03 2017 STATUS approved

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Last modified August 2 06:23 EDT 2021. Contains 346409 sequences. (Running on oeis4.)