Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #7 Mar 22 2024 17:25:44
%S 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 40,63,50,105,16,210,11,420,22,315,44,525,66,140,33,280,99,350,132,
%U 175,198,245,264,385,24,770,27,1540,36,1155,32,2310,13,4620,26
%N 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 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 Sequence is same as A362855 and A368133 until a(57) = 32.
%C Conjectured to be a permutation of the positive integers (A000027), with primorials, primes and prime powers in natural order.
%F 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 a(1) = 1--> a(2) = 2 since 2 is the least primorial exceeding 1.
%e 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 a(3) = 3--> a(4) = 4 since rad(3*4) = rad(12) = 6.
%e a(4) = 4-->a(5) = 6 since rad(4*6) = rad(24) = 6.
%e a(58,59,60,61) = 2310,13,4620,26 = P(5), prime(6), 2*P(5), 2*prime(6).
%Y Cf. A000027, A000040, A000961, A002110, A007947, A362855, A368133.
%K nonn
%O 1,2
%A _David James Sycamore_, Feb 28 2024