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

1,1

Links

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

Formula

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

Example

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.

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 *)

Prog

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

Crossrefs

Subsequence of A013929.

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

Sequence in context: A031484 A260009 A114013 * A161689 A354342 A230653

Adjacent sequences: A235575 A235576 A235577 * A235579 A235580 A235581

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jan 12 2014

Extensions

Terms corrected by Michel Marcus, Jan 12 2014

Status

approved