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%I #40 Nov 16 2023 08:44:52
%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 primes (A000040) as A113877 (Semiprimes to semiprime powers) is to semiprimes (A001358). - _Jonathan Vos Post_, Mar 26 2013; corrected by _M. F. Hasler_, Nov 06 2023
%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
%F A010055(a(n)) * A010051(A100995(a(n))) = 1. - _Reinhard Zumkeller_, Jun 05 2013
%F Sum_{n>=1} 1/a(n) = Sum_{p prime} P(p) = 0.6716752222..., where P is the prime zeta function. - _Amiram Eldar_, Nov 21 2020
%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 (Haskell)
%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.
%Y Cf. A113877 (similar for semiprimes).
%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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