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A347179
a(1) = 1; for n > 1, a(n) = smallest distinct positive integer such that gcd(a(n),a(n-k)) = 1, where k is each divisor of a(n) and n - k >= 1.
3
1, 2, 3, 5, 4, 7, 9, 8, 11, 13, 10, 17, 15, 14, 19, 23, 16, 21, 25, 26, 29, 31, 22, 27, 37, 20, 41, 33, 28, 39, 43, 32, 47, 49, 34, 45, 53, 35, 58, 51, 59, 46, 61, 55, 57, 62, 65, 67, 69, 38, 71, 73, 50, 77, 79, 64, 75, 83, 44, 85, 81, 76, 87, 89, 56, 97, 63, 68, 91, 95, 74, 93, 101, 52, 103
OFFSET
1,2
COMMENTS
The majority of terms are concentrated along two lines, the upper line has gradient of approximately 1.342, while the lower line, which is less well defined, has a gradient of approximately 1.05. See the linked image.
Small numbers with only 2 and 3 as prime divisors apparently take many terms to appear. For example a(64963) = 6, a(80415) = 18, while 12 and 24 have not appeared after 250000 terms.
EXAMPLE
a(3) = 3 as the divisors of 3 are 1 and 3, and a(3-1) = 2 which has no common divisor with 3. As a(3-3) = a(0) is not defined this term is ignored.
a(5) = 4 as the divisors of 4 are 1, 2 and 4, and a(5-1) = a(4) = 5, a(5-2) = a(3) = 3, and a(5-4) = a(1) = 1, and the gcd of 4 and these three numbers is 1.
a(11) = 10 as the divisors of 10 are 1, 2, 5 and 10, and a(11-1) = a(10) = 13, a(11-2) = a(9) = 11, a(11-5) = a(6) = 7, and a(11-10) = a(1) = 1, and the gcd of 10 and these four numbers is 1.
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Scott R. Shannon, Aug 21 2021
STATUS
approved