A364010 -id:A364010 - cp's OEIS frontend

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

Massimo Kofler, Jul 01 2023

nonn

			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.

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

Intersection of A001358 and A281192.

Cf. A013929, A364010.

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

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

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

A362561 Sphenic numbers k such that none of k-2, k-1, k+1 and k+2 is squarefree.

Original entry on oeis.org

170, 530, 638, 874, 962, 1826, 2526, 2674, 2726, 2782, 2874, 3178, 3970, 4490, 4526, 4654, 5930, 6026, 6254, 7138, 7174, 8074, 8126, 8426, 8723, 8958, 8974, 9926, 10286, 10526, 10610, 11222, 11494, 11674, 11710, 11998, 12338, 12626, 12770, 12986, 13574, 15238, 15274, 15326, 15826

Offset: 1

Massimo Kofler, Sep 07 2023

nonn

			168 = 2^3 * 3 * 7, 169 = 13^2, 170 = 2 * 5 * 17, 171 = 3^2 *19, 172 = 2^2 * 43, so 170 is a term.
528 = 2^4 * 3 * 11, 529 = 23^2, 530 = 2 * 5 * 53, 531 = 3^2 * 59, 532 = 2^2 * 7 * 19, so 532 is a term.

Cf. A007304, A013929, A153215, A364010. Subsequence of A364905.

Select[Range[17000], FactorInteger[#][[;; , 2]] == {1, 1, 1} && ! AnyTrue[# + {-2, -1, 1, 2}, SquareFreeQ] &] (* Amiram Eldar, Sep 07 2023 *)

cp's OEIS Frontend

A364025 Semiprimes with no squarefree neighbors.

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