|
| |
|
|
A360017
|
|
Nonsquarefree numbers k such that k - d is also a nonsquarefree number for all proper divisors d of k.
|
|
1
|
|
|
|
25, 50, 125, 169, 243, 289, 325, 343, 351, 361, 425, 605, 625, 725, 729, 841, 845, 925, 1025, 1053, 1325, 1369, 1445, 1450, 1525, 1625, 1681, 1825, 1850, 2125, 2197, 2225, 2401, 2425, 2525, 2725, 2809, 2825, 2873, 3125, 3425, 3625, 3721, 3725, 3757, 3872, 3925, 4205, 4225, 4325, 4525
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
LINKS
|
|
|
|
EXAMPLE
|
The proper divisors of 25 are (1, 5); 25-1 and 25-5 are both nonsquarefree; so 25 is a term.
|
|
|
MATHEMATICA
|
q[n_] := ! SquareFreeQ[n] && AllTrue[Divisors[n], # == n || ! SquareFreeQ[n - #] &]; Select[Range[5000], q] (* Amiram Eldar, Jan 22 2023 *)
|
|
|
PROG
|
(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];
(PARI) isok(k) = if (!issquarefree(k), fordiv(k, d, if (issquarefree(k-d), return(0))); return(1)); \\ Michel Marcus, Jan 22 2023
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
