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A120837
a(n) = the smallest positive integer which does not occur earlier in the sequence and which is coprime to the number of positive divisors of n.
1
1, 3, 5, 2, 7, 9, 11, 13, 4, 15, 17, 19, 21, 23, 25, 6, 27, 29, 31, 35, 33, 37, 39, 41, 8, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 10, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 87, 14, 85, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 12, 115, 117, 119, 121
OFFSET
1,2
COMMENTS
Sequence is a permutation of the positive integers.
Scatterplot shows trajectories of odd numbers, even numbers that are not 3 smooth, 3 smooth numbers that are not 5 smooth, etc. - Michael De Vlieger, Oct 12 2024
LINKS
Michael De Vlieger, Log log scatterplot of a(n), n = 1..2^14, showing primes in red, perfect prime powers in gold, squarefree composites in green, and numbers neither squarefree nor prime powers in blue and purple, where purple also represents powerful numbers that are not prime powers.
EXAMPLE
6 has 4 positive divisors. Among those positive integers not occurring among the first 5 terms of the sequence, 9 is the smallest which is coprime to 4. So a(6) = 9. 4, 6 and 8 also do not occur among the first 5 terms of the sequence, but they are not coprime to 4.
MATHEMATICA
s={1}; Do[i=1; Until[!MemberQ[s, i]&&CoprimeQ[i, DivisorSigma[0, n]], i++]; AppendTo[s, i], {n, 2, 68}]; s (* James C. McMahon, Oct 12 2024 *)
CROSSREFS
Cf. A000005.
Sequence in context: A243352 A026184 A026208 * A208754 A180077 A095749
KEYWORD
nonn
AUTHOR
Leroy Quet, Aug 18 2006
EXTENSIONS
Extended by Ray Chandler, Aug 22 2006
STATUS
approved