A363830 Lesser of 2 successive sphenic numbers (k, k+4) sandwiching 3 consecutive nonsquarefree numbers.

602, 1374, 2274, 2522, 3122, 3282, 4202, 4922, 4958, 4974, 5822, 5885, 6874, 7298, 7674, 9062, 9422, 9474, 10322, 11222, 12590, 13074, 15531, 15722, 16818, 18766, 19131, 19745, 20447, 21535, 22922, 24774, 24938, 25323, 25622, 26522, 26738, 27978, 28034, 28074, 28222

Offset

1,1

Links

Table of n, a(n) for n=1..41.

Example

602 = 2 * 7 * 43 and 606 = 2 * 3 * 101 are sphenic numbers; 603 = 3^2 * 67, 604 = 2^2 * 151 and 605 = 5 * 11^2 are 3 consecutive nonsquarefree numbers, so 602 is a term.
1374 = 2 * 3 * 229 and 1378 = 2 * 13 * 53 are sphenic numbers; 1375 = 5^3 * 11, 1376 = 2^5 * 43 and 1377 = 3^4 * 17 are 3 consecutive nonsquarefree numbers, so 1374 is a term.

Mathematica

Select[Partition[Select[Range[30000], FactorInteger[#][[;; , 2]] == {1, 1, 1} &], 2, 1], Differences[#] == {4} && ! Or @@ SquareFreeQ /@ Range[First[#] + 1, Last[#] - 1] &][[;; , 1]] (* Amiram Eldar, Oct 19 2023 *)

Crossrefs

Cf. A007304, A013929.

Sequence in context: A045940 A124057 A252435 * A045941 A268588 A251462

Adjacent sequences: A363827 A363828 A363829 * A363831 A363832 A363833

Keyword

nonn

Author

Massimo Kofler, Oct 19 2023

Status

approved