OFFSET
0,2
COMMENTS
LINKS
David A. Corneth, Table of n, a(n) for n = 0..12
Dario Alpern, Factorization using the Elliptic Curve Method
FORMULA
Partial products of A113511.
log a(n) ~ (1/3) n^3 log n. [Charles R Greathouse IV, Jan 13 2012]
a(0) = 1; a(n + 1) = A002110(binomial(n + 2, 2)) * a(n). - David A. Corneth, Jan 03 2019
EXAMPLE
The canonical prime factorization of a(3) = 1801800 is 2^3*3^2*5^2*7*11*13. The prime signature of 1801800 is therefore (3,2,2,1,1,1). Note that (3,2,2,1,1,1) contains exactly one number that appears once (3), one number that appears twice (2), and one number that appears three times (1).
MATHEMATICA
Table[Product[Times@@Prime[i*(i-1)/2+Ceiling[Range[i*(n-i)]/(n-i)]], {i, n-1}], {n, 6}] (* Gus Wiseman, Jan 03 2019 *)
PROG
(PARI) a(n) = if(n == 0, return(1)); my(f = matrix(binomial(n+1, 2), 2)); f[, 1] = primes(#f~ )~; f[, 2] = Vecrev(concat(vector(n, i, vector(n+1-i, j, i))))~; factorback(f) \\ David A. Corneth, Jan 03 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Matthew Vandermast, Jan 05 2011
STATUS
approved