cp's OEIS Frontend

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.

%I A347179 #17 Sep 04 2021 20:57:58
%S A347179 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,
%T A347179 20,41,33,28,39,43,32,47,49,34,45,53,35,58,51,59,46,61,55,57,62,65,67,
%U A347179 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
%N 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.
%C A347179 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.
%C A347179 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.
%H A347179 Scott R. Shannon, <a href="/A347179/a347179_1.png">Image of the first 250000 terms</a>.
%e A347179 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.
%e A347179 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.
%e A347179 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.
%Y A347179 Cf. A347406, A027750, A000005, A084937, A098550, A336957.
%K A347179 nonn,look
%O A347179 1,2
%A A347179 _Scott R. Shannon_, Aug 21 2021