A364025 Semiprimes with no squarefree neighbors.

26, 49, 51, 55, 91, 161, 235, 249, 295, 305, 339, 341, 362, 377, 413, 415, 451, 485, 489, 551, 559, 579, 629, 649, 667, 685, 687, 703, 721, 723, 737, 749, 849, 851, 917, 926, 949, 951, 955, 989, 1027, 1057, 1059, 1077, 1079, 1099, 1126, 1133, 1135, 1149, 1169, 1205, 1207, 1211, 1241

Offset: 1

Author

Massimo Kofler, Jul 01 2023

Keywords

• nonn

Examples

			25 = 5^2, 26 = 2 * 13, 27 = 3^3, so 26 is a term.
50 = 2 * 5^2, 51 = 3 * 17, 52 = 2^2 * 13, so 51 is a term.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A001358 and A281192.

Cf. A013929, A364010.

Programs

Maple

filter:= proc(n) uses numtheory; not issqrfree(n-1) and not issqrfree(n+1) and bigomega(n) = 2 end proc:
selest(filter, [$1..2000]); # Robert Israel, Dec 12 2023

Mathematica

Select[Range[1300], PrimeOmega[#] == 2 && ! AnyTrue[# + {-1, 1}, SquareFreeQ] &] (* Amiram Eldar, Jul 01 2023 *)

PARI

isok(k) = (bigomega(k)==2) && !issquarefree(k-1) && !issquarefree(k+1); \\ Michel Marcus, Aug 12 2023