A360017 - OEIS

%I #26 Feb 11 2023 20:31:47

%S 25,50,125,169,243,289,325,343,351,361,425,605,625,725,729,841,845,

%T 925,1025,1053,1325,1369,1445,1450,1525,1625,1681,1825,1850,2125,2197,

%U 2225,2401,2425,2525,2725,2809,2825,2873,3125,3425,3625,3721,3725,3757,3872,3925,4205,4225,4325,4525

%N Nonsquarefree numbers k such that k - d is also a nonsquarefree number for all proper divisors d of k.

%e The proper divisors of 25 are (1, 5); 25-1 and 25-5 are both nonsquarefree; so 25 is a term.

%t q[n_] := ! SquareFreeQ[n] && AllTrue[Divisors[n], # == n || ! SquareFreeQ[n - #] &]; Select[Range[5000], q] (* _Amiram Eldar_, Jan 22 2023 *)

%o (Magma) [n: n in [1..5000] | not IsSquarefree(n) and #[d: d in [1..n-1] | n mod d eq 0 and IsSquarefree(n-d)] eq 0];

%o (PARI) isok(k) = if (!issquarefree(k), fordiv(k, d, if (issquarefree(k-d), return(0))); return(1)); \\ _Michel Marcus_, Jan 22 2023

%Y Cf. A013929 (nonsquarefree numbers), A027751 (proper divisors).

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Jan 21 2023