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Integers having no representation as sum of two nonsquarefree numbers.
2

%I #17 Feb 25 2020 02:11:47

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

%N Integers having no representation as sum of two nonsquarefree numbers.

%C 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.

%H G. L. Honaker, Jr. and Chris K. Caldwell, <a href="https://primes.utm.edu/curios/page.php?curio_id=5071">Prime Curios! 23</a>

%e 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.

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

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

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

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

%K nonn,full,fini

%O 1,2

%A _Bernard Schott_, Feb 23 2020