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A053810 Prime powers of prime numbers. 37
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 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

LINKS

T. D. Noe, Table of n, a(n) for n = 1..9965

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. A000040, A000961, A053811, A053812.

Cf. A203967; subsequence of A000961.

Sequence in context: A093771 A051676 A114129 * A076702 A051761 A153326

Adjacent sequences:  A053807 A053808 A053809 * A053811 A053812 A053813

KEYWORD

easy,nonn,changed

AUTHOR

Henry Bottomley, Mar 28 2000

EXTENSIONS

More terms from David Wasserman, Feb 17 2006

STATUS

approved

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Last modified November 30 21:31 EST 2020. Contains 338813 sequences. (Running on oeis4.)