OFFSET
1,2
COMMENTS
Largest primorial in this sequence is A002110(4) = 210.
The primorials A002110(0..4) are the only squarefree numbers in this sequence.
Not a subset of A060735; a(13) = 2520 is not in A060735. Though common for small n, the set of a(n) in A060735 is likely finite; the restriction is connected with the finite number of primorials in the sequence.
The prime shape of a(n) appears to feature exponents m of prime power factors p^m | a(n) that are nonincreasing as pi(p) increases.
LINKS
Michael S. Branicky, Table of n, a(n) for n = 1..67 (terms 1..56 from Michael De Vlieger)
Michael De Vlieger, Prime power decomposition of A371630(n), n = 1..56.
EXAMPLE
Table of a(n) and A371634(n) = b(n) for n = 1..20. Asterisks in the a(n) column denote squarefree terms while "+" denotes numbers not in A055932 (i.e., in A080259).
n a(n) A067255(a(n)) d(n)-f(n) = b(n)
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1 1* 1 1 - 1 = 0
2 2* 2 2 - 1 = 1
3 6* 2 * 3 4 - 1 = 3
4 12 2^2 * 3 6 - 2 = 4
5 30* 2 * 3 * 5 8 - 1 = 7
6 60 2^2 * 3 * 5 12 - 2 = 10
7 120 2^3 * 3 * 5 16 - 4 = 12
8 210* 2 * 3 * 5 * 7 16 - 1 = 15
9 420 2^2 * 3 * 5 * 7 24 - 2 = 22
10 840 2^3 * 3 * 5 * 7 32 - 4 = 28
11 1260 2^2 * 3^2 * 5 * 7 36 - 6 = 30
12 1680 2^4 * 3 * 5 * 7 40 - 8 = 32
13 2520 2^3 * 3^2 * 5 * 7 48 - 11 = 37
14 4620 2^2 * 3 * 5 * 7 * 11 48 - 2 = 46
15 9240 2^3 * 3 * 5 * 7 * 11 64 - 4 = 60
16 13860 2^2 * 3^2 * 5 * 7 * 11 72 - 6 = 66
17 18480 2^4 * 3 * 5 * 7 * 11 80 - 8 = 72
18 27720 2^3 * 3^2 * 5 * 7 * 11 96 - 12 = 84
19 32760+ 2^3 * 3^2 * 5 * 7 * 13 96 - 11 = 85
20 55440 2^4 * 3^2 * 5 * 7 * 11 120 - 20 = 100
CROSSREFS
KEYWORD
nonn,hard
AUTHOR
Michael De Vlieger, Jun 04 2024
STATUS
approved