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A347933
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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.
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0
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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
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history;
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OFFSET
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1,2
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REFERENCES
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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.
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LINKS
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Table of n, a(n) for n=1..26.
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EXAMPLE
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1 and 2 are the first two terms of the sequence because they can't even be written as sums of three positive integers.
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).
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).
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A224535, A100951, A100952.
Sequence in context: A178860 A178858 A243356 * A117296 A096503 A055238
Adjacent sequences: A347930 A347931 A347932 * A347934 A347935 A347936
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KEYWORD
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nonn,fini,full
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AUTHOR
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José Hernández, Sep 20 2021
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STATUS
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approved
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