A364905 Sphenic numbers with no squarefree neighbors.

170, 530, 595, 638, 651, 665, 874, 962, 1015, 1209, 1495, 1551, 1695, 1749, 1826, 1855, 2035, 2255, 2365, 2431, 2451, 2465, 2526, 2674, 2717, 2726, 2737, 2739, 2751, 2755, 2782, 2849, 2874, 3115, 3145, 3178, 3363, 3367, 3451, 3619, 3655, 3689, 3835, 3905, 3970, 4015, 4017, 4047, 4085

Offset: 1

Author

Massimo Kofler, Aug 12 2023

Keywords

• nonn

Examples

			169 = 13^2, 170 = 2 * 5 * 17, 171 = 3^2 * 19, so 170 is a term.
529 = 53^2, 530 = 2 * 5 * 53, 531 = 3^2 * 59, so 530 is a term.
		

Crossrefs

Intersection of A007304 and A281192.

Cf. A013929, A364025.

Programs

Mathematica

Select[Range[4500], FactorInteger[#][[;; , 2]] == {1, 1, 1} && ! Or @@ SquareFreeQ /@ (# + {-1, 1} ) &] (* Amiram Eldar, Aug 12 2023 *)

PARI

isok(k) = (bigomega(k)==3) && (omega(k)==3) && !issquarefree(k-1) && !issquarefree(k+1); \\ Michel Marcus, Aug 12 2023