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A371630
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Numbers k that set records in A372720.
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3
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1, 2, 6, 12, 30, 60, 120, 210, 420, 840, 1260, 1680, 2520, 4620, 9240, 13860, 18480, 27720, 32760, 55440, 65520, 102960, 110880, 120120, 180180, 240240, 360360, 556920, 720720, 1081080, 1441440, 1884960, 2162160, 2827440, 2882880, 3063060, 3603600, 4084080, 6126120
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OFFSET
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1,2
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COMMENTS
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In other words, numbers k that set records for d(k) - f(k), where d = A000005 and f = A008479.
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.
Not a subset of A025487 or A055932; a(19) = 32760 is the smallest term without a primorial kernel.
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.
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LINKS
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EXAMPLE
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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
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CROSSREFS
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KEYWORD
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nonn,hard
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AUTHOR
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STATUS
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approved
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