A368589 Lesser of 2 successive squarefree semiprimes (k, k+5) sandwiching 4 consecutive nonsquarefree numbers.

3749, 13373, 16574, 20573, 21461, 24449, 51542, 63746, 64049, 79673, 79721, 107846, 110102, 134306, 149642, 155966, 161549, 184922, 201074, 201221, 212021, 228974, 244949, 259073, 270917, 282446, 282533, 283706, 283742, 284246, 295322, 319874, 328346, 343274

Offset

1,1

Links

Table of n, a(n) for n=1..34.

Example

3749 = 23 * 163 and 3754 = 2 * 1877 are squarefree semiprime; 3750 = 2 * 3 * 5^4, 3751 = 11^2 * 31, 3752 = 2^3 * 7 * 67 and 3753 = 3^3 * 139 are 4 consecutive nonsquarefree numbers, so 3749 is a term.
13373 = 43 * 311 and 13378 = 2 * 6689 are squarefree semiprime; 13374 = 2 * 3^2 * 743, 13375 = 5^3 * 107, 13376 = 2^6 * 11 * 19 and 13377 = 3 * 7^3 * 13 are 4 consecutive nonsquarefree numbers, so 13373 is a term.

Mathematica

Select[Partition[Select[Range[350000], SquareFreeQ], 2, 1], Differences[#] == {5} && PrimeOmega[#] == {2, 2} &][[;; , 1]] (* Amiram Eldar, Dec 31 2023 *)

Crossrefs

Cf. A006881, A013929, A363821.

Sequence in context: A340403 A235977 A235243 * A180974 A285158 A238031

Adjacent sequences: A368585 A368586 A368587 * A368590 A368591 A368592

Keyword

nonn

Author

Massimo Kofler, Dec 31 2023

Status

approved