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 A053810 Prime powers of prime numbers. 36

%I

%S 4,8,9,25,27,32,49,121,125,128,169,243,289,343,361,529,841,961,1331,

%T 1369,1681,1849,2048,2187,2197,2209,2809,3125,3481,3721,4489,4913,

%U 5041,5329,6241,6859,6889,7921,8192,9409,10201,10609,11449,11881,12167

%N Prime powers of prime numbers.

%C This is to triprimes as A053810 (Prime powers of prime numbers) is to primes and as semiprimes are to A113877 (Semiprimes to semiprime powers). - _Jonathan Vos Post_, Mar 26 2013

%C A010055(a(n)) * A010051(A100995(a(n))) = 1. - _Reinhard Zumkeller_, Jun 05 2013

%H T. D. Noe, <a href="/A053810/b053810.txt">Table of n, a(n) for n = 1..9965</a>

%F a(n) = A053811(n)^A053812(n). - _David Wasserman_, Feb 17 2006

%t pp={}; Do[if=FactorInteger[n]; If[Length[if]==1&&PrimeQ[if[[1, 1]]]&&PrimeQ[if[[1, 2]]], pp=Append[pp, n]], {n, 13000}]; pp

%t Sort[ Flatten[ Table[ Prime[n]^Prime[i], {n, 1, PrimePi[ Sqrt[12800]]}, {i, 1, PrimePi[ Log[ Prime[n], 12800]]}]]]

%o (PARI) is(n)=isprime(isprimepower(n)) \\ _Charles R Greathouse IV_, Mar 19 2013

%o a053810 n = a053810_list !! (n-1)

%o a053810_list = filter ((== 1) . a010051 . a100995) \$ tail a000961_list

%o -- _Reinhard Zumkeller_, Jun 05 2013

%Y Cf. A000040, A000961, A053811, A053812.

%Y Cf. A203967; subsequence of A000961.

%K easy,nonn

%O 1,1

%A _Henry Bottomley_, Mar 28 2000

%E More terms from _David Wasserman_, Feb 17 2006

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Last modified March 29 02:19 EDT 2020. Contains 333104 sequences. (Running on oeis4.)