A166475 4th level primorials: product of first n superduperprimorials.

1, 2, 48, 414720, 270888468480000, 30900096179361042923520000000000, 1848494880770448654906901042987600267878400000000000000000000

Offset

0,2

Comments

Next term has 110 digits.

a(n) = first counting number with n distinct positive tetrahedral exponents in its prime factorization (cf. A000292).

Note: a(n) is not the first counting number with n distinct square exponents in its prime factorization, as previously stated. That sequence is A212170. - Matthew Vandermast, May 23 2012

Links

Table of n, a(n) for n=0..6.

Dario Alpern, Factorization using the Elliptic Curve Method

Formula

a(n) = Product_{k=1..n} prime(k)^((n-k+1)^2).

Example

a(3) = 414720 = 2^10*3^4*5^1 has 3 positive tetrahedral exponents in its prime factorization (cf. A000292).  It is the smallest number with this property.

Crossrefs

Subsequence of A025487.

Cf. A002110, A006939, A066120 for first, second and third level primorials.

Sequence in context: A344665 A212170 A057527 * A152688 A046873 A261125

Adjacent sequences: A166472 A166473 A166474 * A166476 A166477 A166478

Keyword

nonn,easy

Author

Matthew Vandermast, Nov 05 2009

Extensions

Offset corrected by Matthew Vandermast, Nov 07 2009

Edited by Matthew Vandermast, Nov 10 2009, May 23 2012

Name changed by Arkadiusz Wesolowski, Feb 21 2014

Status

approved