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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..10000

EXAMPLE

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.

MATHEMATICA

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

PROG

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