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A370740 a(1) = 1. Thereafter a(n) is the least novel k such that A007947(k*a(n-1)) is the smallest number in A002110 which is not already a term.

%I A370740 #7 Mar 22 2024 17:25:44
%S A370740 1,2,3,4,6,5,12,10,9,20,15,8,30,7,60,14,45,28,75,42,25,84,35,18,70,21,
%T A370740 40,63,50,105,16,210,11,420,22,315,44,525,66,140,33,280,99,350,132,
%U A370740 175,198,245,264,385,24,770,27,1540,36,1155,32,2310,13,4620,26
%N A370740 a(1) = 1. Thereafter a(n) is the least novel k such that A007947(k*a(n-1)) is the smallest number in A002110 which is not already a term.
%C A370740 In other words, for n > m, where a(m) = A002110(r), a(n) is the least novel k such that rad(k*a(n-1)) = A002110(r+1).
%C A370740 Sequence is same as A362855 and A368133 until a(57) = 32.
%C A370740 Conjectured to be a permutation of the positive integers (A000027), with primorials, primes and prime powers in natural order.
%F A370740 For m >= 1, a(n) = P(m) = A002110(m)-->a(n+1) = prime(m+1), a(n+2) = 2*P(m), a(n+3) = 2*prime(m+1); (see last in Example).
%e A370740 a(1) = 1--> a(2) = 2 since 2 is the least primorial exceeding 1.
%e A370740 a(2) = 2--> a(3) = 3 since 2*3 = 6, the next primorial, and no k < 3 is such that rad(k*2) = 6.
%e A370740 a(3) = 3--> a(4) = 4 since rad(3*4) = rad(12) = 6.
%e A370740 a(4) = 4-->a(5) = 6 since rad(4*6) = rad(24) = 6.
%e A370740 a(58,59,60,61) = 2310,13,4620,26 = P(5), prime(6), 2*P(5), 2*prime(6).
%Y A370740 Cf. A000027, A000040, A000961, A002110, A007947, A362855, A368133.
%K A370740 nonn
%O A370740 1,2
%A A370740 _David James Sycamore_, Feb 28 2024