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.

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

Author

Scott R. Shannon, Aug 21 2021

Keywords

• nonn
• look

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.

Examples

			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.
		

Links

• Scott R. Shannon, Image of the first 250000 terms.

Crossrefs

Cf. A347406, A027750, A000005, A084937, A098550, A336957.