A363821 Lesser of 2 successive squarefree semiprimes (k, k+4) sandwiching 3 consecutive nonsquarefree numbers.

1923, 2573, 2823, 3427, 3574, 3869, 3949, 4474, 4849, 4911, 5191, 5489, 5633, 5947, 6927, 7153, 7323, 7397, 7405, 7441, 7747, 7985, 8223, 8347, 8403, 8917, 9249, 9385, 9557, 9773, 10042, 10447, 10673, 10681, 11659, 12219, 13349, 13423, 13849, 14209, 14273, 16323, 16973

Offset

1,1

Links

Table of n, a(n) for n=1..43.

Example

1923 = 3 * 641 and 1927 = 41 * 47 are semiprime numbers; 1924 = 2^2 * 13 * 37, 1925 = 5^2 * 7 * 11 and 1926 = 2 * 3^2 * 107 are 3 consecutive nonsquarefree numbers, so 1923 is a term.
2573 = 31 * 83 and 2577 = 3 * 859 are semiprime numbers; 2574 = 2 * 3^2 * 11 * 13, 2575 = 5^2 * 103 and 2576 = 2^4 * 7 * 23 are 3 consecutive nonsquarefree numbers, so 2573 is a term.

Mathematica

Select[Partition[Select[Range[17000], SquareFreeQ], 2, 1], Differences[#] == {4} && PrimeOmega[#] == {2, 2} &][[;; , 1]] (* Amiram Eldar, Oct 18 2023 *)

Prog

(PARI) is1(n) = (bigomega(n)==2) && (omega(n)==2); \\ A006881
is9(n) = !issquarefree(n); \\ A013929
isok(k) = is1(k) && is9(k+1) && is9(k+2) && is9(k+3) && is1(k+4); \\ Michel Marcus, Oct 22 2023

Crossrefs

Cf. A006881, A013929.

Sequence in context: A035768 A107564 A135648 * A255867 A326018 A202051

Adjacent sequences: A363818 A363819 A363820 * A363822 A363823 A363824

Keyword

nonn

Author

Massimo Kofler, Oct 18 2023

Status

approved