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

%I A166502 #14 May 05 2019 03:51:58
%S A166502 6,225,42875,35153041,59797108943,116507435287321,366790143213462347,
%T A166502 1329999555322686599521,26129584584668699724236347,
%U A166502 344823548950275944213556441001,4520615782446712879799718786455203,148534373731547764810930925932451123761
%N A166502 The n-th power of the product prime(n)*prime(n+1) of 2 successive primes.
%H A166502 Harvey P. Dale, <a href="/A166502/b166502.txt">Table of n, a(n) for n = 1..166</a>
%F A166502 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 A166502 a(n) = A006094(n)^n. - _Michel Marcus_, May 05 2019
%e A166502 A[k,n] = n-th product of k-th power of 2 successive primes begins:
%e A166502 ===============================================================================
%e A166502 ...|.n=1|..n=2|....n=3|.....n=4|......n=5|......n=6|......n=7|......n=8|.in.OEIS
%e A166502 ================================================================================
%e A166502 k=1|...6|...15|.....35|......77|......143|......221|......323|......437|A006094
%e A166502 k=2|..36|..225|...1225|....5929|....20449|....48841|...104329|...104329|A166329
%e A166502 k=3|.216|.3375|..42875|..456533|..2924207|.10793861|.33698267|.83453453|A152241
%e A166502 k=4|1296|50625|1500625|35153041|418161601|.........|.........|.........|.......
%e A166502 ================================================================================
%p A166502 A166502 := proc(n) ithprime(n)*ithprime(n+1) ; %^n ; end: seq(A166502(n),n=1..15) ; # _R. J. Mathar_, Oct 16 2009
%t A166502 With[{nn=20},(Times@@#[[2]])^#[[1]]&/@Thread[{Range[nn-1],Partition[ Prime[ Range[ nn]],2,1]}]] (* _Harvey P. Dale_, Jan 12 2015 *)
%o A166502 (PARI) a(n) = (prime(n)*prime(n+1))^n; \\ _Michel Marcus_, May 05 2019
%Y A166502 Cf. A000040, A006094, A166329, A152241.
%K A166502 easy,nonn
%O A166502 1,1
%A A166502 _Jonathan Vos Post_, Oct 15 2009