A331802 Integers having no representation as sum of two nonsquarefree numbers.

1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 14, 15, 19, 23

Offset

1,2

Comments

This sequence is finite with 14 terms and 23 is the largest term (see Prime Curios link); a proof can be found in comments of A331801.

Links

Table of n, a(n) for n=1..14.

G. L. Honaker, Jr. and Chris K. Caldwell, Prime Curios! 23

Example

With the two smallest nonsquarefree numbers 4 and 8, it is not possible to get 1, 2, 3, 4, 5, 6, 7, 9, 10 and 11 as sum of two nonsquarefree numbers.

Mathematica

max = 25; Complement[Range[max], Union @ Select[Total /@ Tuples[Select[Range[max], !SquareFreeQ[#] &], 2], # <= max &]] (* Amiram Eldar, Feb 24 2020 *)

Crossrefs

Cf. A005117 (squarefree), A013929 (nonsquarefree), A331801 (complement).

Cf. A000404 (sum of 2 nonzero squares), A018825 (not the sum of 2 nonzero squares).

Cf. A001694 (squareful), A052485 (not squareful), A076871 (sum of 2 squareful), A085253 (not the sum of 2 squareful).

Sequence in context: A272570 A123101 A071557 * A271108 A179401 A117729

Adjacent sequences: A331799 A331800 A331801 * A331803 A331804 A331805

Keyword

nonn,full,fini

Author

Bernard Schott, Feb 23 2020

Status

approved