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

1,1

Links

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

Example

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.

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 *)

Prog

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

Crossrefs

Intersection of A001358 and A281192.

Cf. A013929, A364010.

Sequence in context: A118367 A316120 A261932 * A324041 A375139 A137263

Adjacent sequences: A364022 A364023 A364024 * A364026 A364027 A364028

Keyword

nonn

Author

Massimo Kofler, Jul 01 2023

Status

approved