A131690 a(n) = Product_{k=1..n} A008578(k)^A008578(n-k+1).

1, 2, 12, 360, 151200, 2095632000, 7551819475200000, 7286477990937425280000000, 16326289449604557795871699200000000000, 48235535472088469901966394717904245153920000000000000, 1927704301314417844667587261525561805756528196513768633600000000000000000

Offset: 1

Author

Darse Billings, Sep 14 2007

Keywords

• nonn

Comments

Exponents of the prime factorization are the primes in reverse order. Similar to A087315, but where the largest prime factor has an exponent of one instead of two (and 1^n is understood to be the first term).

Examples

			a(5) = 1^7 * 2^5 * 3^3 * 5^2 * 7^1 = 151200.
		

Crossrefs

Cf. A008578, A087315, A076265, A076265.

Programs

Mathematica

s={};Do[p1=Join[{1},Prime[Range[n-1]]];AppendTo[s,Product[p1[[k]]^p1[[n-k+1]],{k,n}]],{n,11}];s (* James C. McMahon, Feb 27 2025 *)

Formula

a(n) = Product_{k=1..n} A008578(k)^A008578(n-k+1) where A008578 is the sequence of primes prepended with 1.

Extensions

a(11) from James C. McMahon, Feb 27 2025