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.

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, 40, 63, 50, 105, 16, 210, 11, 420, 22, 315, 44, 525, 66, 140, 33, 280, 99, 350, 132, 175, 198, 245, 264, 385, 24, 770, 27, 1540, 36, 1155, 32, 2310, 13, 4620, 26

Offset: 1

Author

David James Sycamore, Feb 28 2024

Keywords

• nonn

Comments

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).

Sequence is same as A362855 and A368133 until a(57) = 32.

Conjectured to be a permutation of the positive integers (A000027), with primorials, primes and prime powers in natural order.

Examples

			a(1) = 1--> a(2) = 2 since 2 is the least primorial exceeding 1.
a(2) = 2--> a(3) = 3 since 2*3 = 6, the next primorial, and no k < 3 is such that rad(k*2) = 6.
a(3) = 3--> a(4) = 4 since rad(3*4) = rad(12) = 6.
a(4) = 4-->a(5) = 6 since rad(4*6) = rad(24) = 6.
a(58,59,60,61) = 2310,13,4620,26 = P(5), prime(6), 2*P(5), 2*prime(6).
		

Crossrefs

Cf. A000027, A000040, A000961, A002110, A007947, A362855, A368133.

Formula

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).