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

Author

Bernard Schott, Feb 23 2020

Keywords

• nonn
• full
• fini

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.

Examples

			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.
		

Links

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

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).

Programs

Mathematica

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