The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A036454 Prime powers with special exponents: q^(p-1) where p > 2 and q are prime numbers. 7
 4, 9, 16, 25, 49, 64, 81, 121, 169, 289, 361, 529, 625, 729, 841, 961, 1024, 1369, 1681, 1849, 2209, 2401, 2809, 3481, 3721, 4096, 4489, 5041, 5329, 6241, 6889, 7921, 9409, 10201, 10609, 11449, 11881, 12769, 14641, 15625, 16129, 17161, 18769, 19321 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Composite numbers with a prime number of divisors. (1 - A010051(a(n))) * A010055(a(n)) * A010051(A100995(a(n))+1) = 1. - Reinhard Zumkeller, Jun 05 2013 LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 FORMULA d(d(a(n))) = 2, where d(x) = tau(x) = sigma_0(x) is the number of divisors of x. a(n) = (n log n)^2 + 2n^2 log n log log n + O(n^2 log n). - Charles R Greathouse IV, Apr 26 2012 A036459(a(n)) = 2. - Ivan Neretin, Jan 25 2016 EXAMPLE From powers of 2: 4,16,64,1024,4096,65536 are in the sequence since exponent+1 is also prime. The same powers of any prime base are also included. MAPLE N:= 10^5: P1:= select(isprime, [2, seq(2*i+1, i=1..floor((sqrt(N)-1)/2))]): P2:= select(`<=`, P1, 1+ilog2(N))[2..-1]: S:= {seq(seq(p^(q-1), q = select(`<=`, P2, 1+floor(log[p](N)))), p=P1)}: sort(convert(S, list)); # Robert Israel, May 18 2015 MATHEMATICA specialPrimePowerQ[n_] := With[{f = FactorInteger[n]}, Length[f] == 1 && PrimeQ[f[[1, 1]]] && f[[1, 2]] > 1 && PrimeQ[f[[1, 2]] + 1]]; Select[Range[20000], specialPrimePowerQ]  (* Jean-François Alcover, Jul 02 2013 *) Select[Range[20000], ! PrimeQ[#] && PrimeQ[DivisorSigma[0, #]] &] (* Carlos Eduardo Olivieri, May 18 2015 *) PROG (PARI) for(n=1, 34000, if(isprime(n), n++, x=numdiv(n); if(isprime(x), print(n)))) (PARI) list(lim)=my(v=List(), t); lim=lim\1+.5; forprime(p=3, log(lim)\log(2) +1, t=p-1; forprime(q=2, lim^(1/t), listput(v, q^t))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Apr 26 2012 (Haskell) a009087 n = a009087_list !! (n-1) a009087_list = filter ((== 1) . a010051 . (+ 1) . a100995) a000961_list -- Reinhard Zumkeller, Jun 05 2013 (MAGMA) [n: n in [1..20000] | not IsPrime(n) and IsPrime(DivisorSigma(0, n))]; // Vincenzo Librandi, May 19 2015 CROSSREFS Cf. A000005, A036450, A036452, A010553, A009087. Cf. A002808. Sequence in context: A075494 A063735 A056798 * A115648 A082522 A279096 Adjacent sequences:  A036451 A036452 A036453 * A036455 A036456 A036457 KEYWORD nonn,easy,nice AUTHOR STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified February 26 21:58 EST 2020. Contains 332295 sequences. (Running on oeis4.)