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%I #21 Oct 20 2021 15:11:10
%S 1,2,3,4,5,6,7,8,9,10,12,14,15,16,18,20,22,24,30,36,42,48,60,84,90,210
%N Positive integers that can't be written in the form a+b+c for some positive integers a, b, and c satisfying gcd(a,b)=1, gcd(a,c)>1, and gcd(b,c)>1.
%D Freddy Barrera, Bernardo Recamán, and Stan Wagon, Sums of triples with one pair relatively prime. American Mathematical Monthly, 127 (2020), no. 1, pp. 89-90.
%e 1 and 2 are the first two terms of the sequence because they can't even be written as sums of three positive integers.
%e 3 is the third term of the sequence because there is only one way to express it as a sum of three positive integers (1+1+1).
%e 11 does not belong to the sequence because 11=2+3+6 (and gcd(2,3)=1, gcd(2,6)=2, and gcd(3,6)=3).
%t Select[Range@210,Select[Flatten[Permutations/@IntegerPartitions[#,{3}],1],GCD[#[[1]],#[[2]]]==1&&GCD[#[[1]],#[[3]]]>1&&GCD[#[[2]],#[[3]]]>1&]=={}&] (* _Giorgos Kalogeropoulos_, Sep 20 2021 *)
%Y Cf. A224535, A100951, A100952.
%K nonn,fini,full
%O 1,2
%A _José Hernández_, Sep 20 2021
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