A360017 Nonsquarefree numbers k such that k - d is also a nonsquarefree number for all proper divisors d of k.

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

Offset

1,1

Links

Table of n, a(n) for n=1..51.

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

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

Sequence in context: A224670 A045195 A232438 * A034025 A253017 A042236

Adjacent sequences: A360014 A360015 A360016 * A360018 A360019 A360020

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jan 21 2023

Status

approved