A368778 - OEIS

A368778

Lesser of 2 successive squarefree semiprimes (k, k+6) sandwiching 5 consecutive nonsquarefree numbers.

843, 1679, 19939, 23271, 33171, 47723, 58847, 68647, 84327, 84571, 102623, 104271, 116763, 119347, 143223, 148523, 163951, 190967, 191147, 205747, 209571, 212191, 213783, 222603, 235247, 245047, 247147, 260971, 276649, 278367, 293947, 294487, 297771, 298823, 310847

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..35.

EXAMPLE

843 = 3 * 281 and 849 = 3 * 283 are squarefree semiprimes; 844 = 2^2 * 211, 845 = 5 * 13^2, 846 = 2 * 3^2 * 47, 847 = 7 * 11^2 and 848 = 2^4 * 53 are 5 consecutive nonsquarefree numbers, so 843 is a term.

1679 = 23 * 73 and 1685 = 5 * 337 are squarefree semiprimes; 1680 = 2^4 * 3 * 5 * 7, 1681 = 41^2, 1682 = 2 * 29^2, 1683 = 3^2 * 11 * 17 and 1684 = 2^2 * 421 are 5 consecutive nonsquarefree numbers, so 1679 is a term.

MATHEMATICA

Select[Partition[Select[Range[300000], SquareFreeQ], 2, 1], Differences[#] == {6} && PrimeOmega[#] == {2, 2} &][[;; , 1]] (* Amiram Eldar, Jan 05 2024 *)

CROSSREFS

Cf. A006881, A013929, A363821.

Sequence in context: A031527 A252568 A045243 * A096025 A004969 A004949

Adjacent sequences: A368775 A368776 A368777 * A368779 A368780 A368781

KEYWORD

nonn

AUTHOR

Massimo Kofler, Jan 05 2024

STATUS

approved