A153215 -id:A153215 - cp's OEIS frontend

A364010 Semiprimes k such that none of k-2, k-1, k+1, and k+2 is squarefree.

26, 362, 926, 1027, 1126, 1574, 1774, 1814, 2059, 2402, 3482, 3574, 4166, 4474, 5042, 5045, 5374, 5426, 5914, 6274, 6326, 6418, 6626, 6649, 7226, 7694, 7985, 8182, 8674, 9026, 9458, 9557, 9874, 9946, 10774, 10826, 11851, 12223, 12494, 12574, 12949, 13349, 13474, 13526, 13582

Offset: 1

Massimo Kofler, Jul 01 2023

nonn

			24 = 2^3 * 3, 25 = 5^2, 26 = 2 * 13, 27 = 3^3, 28 = 2^2 * 7, so 26 is a term.
360 = 2^3 * 3^2 * 5, 361 = 19^2, 362 = 2 * 181, 363 = 3 * 11^2, 364 = 2^2 * 7 * 13, so 362 is a term.

Cf. A001358, A013929, A153215. Subsequence of A364025.

Select[Range[14000], PrimeOmega[#] == 2 && ! AnyTrue[# + {-2, -1, 1, 2}, SquareFreeQ] &] (* Amiram Eldar, Jul 01 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

A364010 Semiprimes k such that none of k-2, k-1, k+1, and k+2 is squarefree.

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