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Sphenic numbers with no squarefree neighbors.
1

%I #19 Sep 06 2023 21:13:53

%S 170,530,595,638,651,665,874,962,1015,1209,1495,1551,1695,1749,1826,

%T 1855,2035,2255,2365,2431,2451,2465,2526,2674,2717,2726,2737,2739,

%U 2751,2755,2782,2849,2874,3115,3145,3178,3363,3367,3451,3619,3655,3689,3835,3905,3970,4015,4017,4047,4085

%N Sphenic numbers with no squarefree neighbors.

%e 169 = 13^2, 170 = 2 * 5 * 17, 171 = 3^2 * 19, so 170 is a term.

%e 529 = 53^2, 530 = 2 * 5 * 53, 531 = 3^2 * 59, so 530 is a term.

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

%o (PARI) isok(k) = (bigomega(k)==3) && (omega(k)==3) && !issquarefree(k-1) && !issquarefree(k+1); \\ _Michel Marcus_, Aug 12 2023

%Y Intersection of A007304 and A281192.

%Y Cf. A013929, A364025.

%K nonn

%O 1,1

%A _Massimo Kofler_, Aug 12 2023