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A053810 Prime powers of prime numbers. 47
4, 8, 9, 25, 27, 32, 49, 121, 125, 128, 169, 243, 289, 343, 361, 529, 841, 961, 1331, 1369, 1681, 1849, 2048, 2187, 2197, 2209, 2809, 3125, 3481, 3721, 4489, 4913, 5041, 5329, 6241, 6859, 6889, 7921, 8192, 9409, 10201, 10609, 11449, 11881, 12167 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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
LINKS
FORMULA
a(n) = A053811(n)^A053812(n). - David Wasserman, Feb 17 2006
A010055(a(n)) * A010051(A100995(a(n))) = 1. - Reinhard Zumkeller, Jun 05 2013
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
MATHEMATICA
pp={}; Do[if=FactorInteger[n]; If[Length[if]==1&&PrimeQ[if[[1, 1]]]&&PrimeQ[if[[1, 2]]], pp=Append[pp, n]], {n, 13000}]; pp
Sort[ Flatten[ Table[ Prime[n]^Prime[i], {n, 1, PrimePi[ Sqrt[12800]]}, {i, 1, PrimePi[ Log[ Prime[n], 12800]]}]]]
PROG
(PARI) is(n)=isprime(isprimepower(n)) \\ Charles R Greathouse IV, Mar 19 2013
(Haskell)
a053810 n = a053810_list !! (n-1)
a053810_list = filter ((== 1) . a010051 . a100995) $ tail a000961_list
-- Reinhard Zumkeller, Jun 05 2013
CROSSREFS
Cf. A203967; subsequence of A000961.
Cf. A113877 (similar for semiprimes).
Sequence in context: A371223 A051676 A114129 * A076702 A051761 A153326
KEYWORD
easy,nonn
AUTHOR
Henry Bottomley, Mar 28 2000
EXTENSIONS
More terms from David Wasserman, Feb 17 2006
STATUS
approved

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Last modified March 28 12:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)