A235578 Squareful numbers with squareful neighbors.

49, 99, 125, 243, 244, 343, 351, 424, 476, 549, 604, 725, 775, 845, 846, 847, 1025, 1251, 1275, 1324, 1376, 1421, 1449, 1520, 1665, 1675, 1681, 1682, 1683, 1849, 1863, 1925, 2008, 2024, 2057, 2107, 2151, 2224, 2276, 2349, 2367, 2524, 2528, 2575, 2645, 2825

Offset: 1

Author

Juri-Stepan Gerasimov, Jan 12 2014

Keywords

• nonn

Examples

			243 is in the sequence because 242 = 2 * 11^2, 243 = 3^5, 244 = 2^2 * 61.
244 is also in the sequence because 245 = 5 * 7^2.
But 245 is not in the sequence because 246 = 2 * 3 * 41.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A013929.

Cf. A001694, A070258, A228649 (squarefree numbers with squarefree neighbors).

Programs

Mathematica

Select[Range@3051, And @@ Not /@ SquareFreeQ /@ {#-1, #, #+1} &] (* Giovanni Resta, Jan 12 2014 *)
Select[Range[2000], Union[MoebiusMu[{# - 1, #, # + 1}]] == {0} &] (* Alonso del Arte, Jan 12 2014 *)

PARI

isok(n) = !issquarefree(n) && !issquarefree(n-1) && !issquarefree(n+1); \\ Michel Marcus, Jan 12 2014

Formula

a(n) = A070258(n) + 1. - Amiram Eldar, Feb 09 2021

Extensions

Terms corrected by Michel Marcus, Jan 12 2014