A166502 - OEIS

%I #14 May 05 2019 03:51:58

%S 6,225,42875,35153041,59797108943,116507435287321,366790143213462347,

%T 1329999555322686599521,26129584584668699724236347,

%U 344823548950275944213556441001,4520615782446712879799718786455203,148534373731547764810930925932451123761

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

%H Harvey P. Dale, <a href="/A166502/b166502.txt">Table of n, a(n) for n = 1..166</a>

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

%F a(n) = A006094(n)^n. - _Michel Marcus_, May 05 2019

%e A[k,n] = n-th product of k-th power of 2 successive primes begins:

%e ===============================================================================

%e ...|.n=1|..n=2|....n=3|.....n=4|......n=5|......n=6|......n=7|......n=8|.in.OEIS

%e ================================================================================

%e k=1|...6|...15|.....35|......77|......143|......221|......323|......437|A006094

%e k=2|..36|..225|...1225|....5929|....20449|....48841|...104329|...104329|A166329

%e k=3|.216|.3375|..42875|..456533|..2924207|.10793861|.33698267|.83453453|A152241

%e k=4|1296|50625|1500625|35153041|418161601|.........|.........|.........|.......

%e ================================================================================

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

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

%o (PARI) a(n) = (prime(n)*prime(n+1))^n; \\ _Michel Marcus_, May 05 2019

%Y Cf. A000040, A006094, A166329, A152241.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Oct 15 2009