

A347933


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.


0



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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OFFSET

1,2


REFERENCES

Freddy Barrera, Bernardo Recamán, and Stan Wagon, Sums of triples with one pair relatively prime. American Mathematical Monthly, 127 (2020), no. 1, pp. 8990.


LINKS

Table of n, a(n) for n=1..26.


EXAMPLE

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).


MATHEMATICA

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 *)


CROSSREFS

Cf. A224535, A100951, A100952.
Sequence in context: A178860 A178858 A243356 * A117296 A096503 A055238
Adjacent sequences: A347930 A347931 A347932 * A347934 A347935 A347936


KEYWORD

nonn,fini,full


AUTHOR

José Hernández, Sep 20 2021


STATUS

approved



