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A138534
Super least prime signatures; LCM of all signatures with n factors.
7
1, 2, 12, 120, 5040, 110880, 43243200, 1470268800, 1173274502400, 269853135552000, 516498901446528000, 32022931889684736000, 3234636350177055183360000, 265240180714518525035520000, 1163343432613878250805790720000, 6014485546613750556665938022400000
OFFSET
0,2
COMMENTS
Also the row product of the following table:
1
2
4 3
8 3 5
16 9 5 7
32 9 5 7 11
64 27 25 7 11 13
128 27 25 7 11 13 17
256 81 25 49 11 13 17 19
512 81 125 49 11 13 17 19 23
1024 243 125 49 121 13 17 19 23 29
...
LINKS
Angelo B. Mingarelli, Abstract factorials, Notes on Number Theory and Discrete Mathematics, Vol. 19, No. 4 (2013), pp. 43-76; arXiv preprint, arXiv:0705.4299 [math.NT], 2007-2012.
FORMULA
From Amiram Eldar, Jul 02 2021: (Start)
a(n) = Product_{k=1..n} prime(k)^floor(n/k).
A001222(a(n)) = A006218(n). (End)
Sum_{n>=0} 1/a(n) = A346044. - Amiram Eldar, Jul 02 2023
EXAMPLE
For n = 3 the signatures are {8, 12, 30} so a(3) = 120.
MAPLE
b:= proc(n, i) option remember; `if`(n=0 or i<2, 2^n,
ilcm(seq(b(n-i*j, i-1)*ithprime(i)^j, j=0..n/i)))
end:
a:= n-> b(n$2):
seq(a(n), n=0..17); # Alois P. Heinz, May 15 2015
MATHEMATICA
b[n_, i_] := b[n, i] = If[n == 0 || i < 2, 2^n, LCM @@ Table[b[n - i j, i - 1] Prime[i]^j, {j, 0, n/i}]];
a[n_] := b[n, n];
a /@ Range[0, 17] (* Jean-François Alcover, Nov 02 2020, after Alois P. Heinz *)
a[n_] := Product[Prime[k]^Floor[n/k], {k, 1, n}]; Array[a, 16, 0] (* Amiram Eldar, Jul 02 2021 *)
PROG
(PARI) a(n) = prod(k=1, n, prime(k)^(n\k)); \\ Michel Marcus, Jul 03 2021
CROSSREFS
Subsequence of A025487.
LCM of terms in rows of A215366.
Sequence in context: A373433 A229901 A007132 * A062080 A221279 A165300
KEYWORD
nonn
AUTHOR
Alford Arnold, Mar 28 2008
EXTENSIONS
More terms from Reikku Kulon, Oct 02 2008
STATUS
approved