A166502 The n-th power of the product prime(n)*prime(n+1) of 2 successive primes.

6, 225, 42875, 35153041, 59797108943, 116507435287321, 366790143213462347, 1329999555322686599521, 26129584584668699724236347, 344823548950275944213556441001, 4520615782446712879799718786455203, 148534373731547764810930925932451123761

Offset: 1

Author

Jonathan Vos Post, Oct 15 2009

Keywords

• easy
• nonn

Examples

			A[k,n] = n-th product of k-th power of 2 successive primes begins:
===============================================================================
...|.n=1|..n=2|....n=3|.....n=4|......n=5|......n=6|......n=7|......n=8|.in.OEIS
================================================================================
k=1|...6|...15|.....35|......77|......143|......221|......323|......437|A006094
k=2|..36|..225|...1225|....5929|....20449|....48841|...104329|...104329|A166329
k=3|.216|.3375|..42875|..456533|..2924207|.10793861|.33698267|.83453453|A152241
k=4|1296|50625|1500625|35153041|418161601|.........|.........|.........|.......
================================================================================
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..166

Crossrefs

Cf. A000040, A006094, A166329, A152241.

Programs

Maple

A166502 := proc(n) ithprime(n)*ithprime(n+1) ; %^n ; end: seq(A166502(n),n=1..15) ; # R. J. Mathar, Oct 16 2009

Mathematica

With[{nn=20},(Times@@#[[2]])^#[[1]]&/@Thread[{Range[nn-1],Partition[ Prime[ Range[ nn]],2,1]}]] (* Harvey P. Dale, Jan 12 2015 *)

PARI

a(n) = (prime(n)*prime(n+1))^n; \\ Michel Marcus, May 05 2019

Formula

a(n) = Product_{i=n..n+1} prime(i)^n = (A000040(n)*A000040(n+1))^n. [corrected by R. J. Mathar, Oct 16 2009]

a(n) = A006094(n)^n. - Michel Marcus, May 05 2019