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 A010055 1 if n is a prime power p^k (k >= 0), otherwise 0. 94
 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Characteristic function of unit or prime powers p^k (k >= 1). Characteristic function of prime powers p^k (k >= 0). - Daniel Forgues, Mar 03 2009 See A065515 for partial sums. - Reinhard Zumkeller, Nov 22 2009 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 FORMULA Dirichlet generating function: 1 + ppzeta(s). Here ppzeta(s) = Sum_{p prime} Sum_{k>=1} 1/(p^k)^s. Note that ppzeta(s) = Sum_{p prime} 1/(p^s-1) = Sum_{k>=1} primezeta(k*s). - Franklin T. Adams-Watters, Sep 11 2005 a(n) = 0^(A119288(n)-1). - Reinhard Zumkeller, May 13 2006 a(A000961(n)) = 1; a(A024619(n)) = 0. - Reinhard Zumkeller, Nov 17 2011 a(n) = if A001221(n) <= 1 then 1, otherwise 0. - Reinhard Zumkeller, Nov 28 2015 If n >= 2, a(n) = A069513(n). - Jeppe Stig Nielsen, Feb 02 2016 Conjecture: a(n) = (n - A048671(n))/A000010(n) for all n > 1. - Velin Yanev, Mar 10 2021 [The conjecture is true. - Andrey Zabolotskiy, Mar 11 2021] MAPLE A010055 := proc(n) if n =1 then 1; else if nops(ifactors(n)[2]) = 1 then 1; else 0 ; end if; end if; end proc: # R. J. Mathar, May 25 2017 MATHEMATICA A010055[n_]:=Boole[PrimeNu[n]<=1]; A010055/@Range[20] (* Enrique Pérez Herrero, May 30 2011 *) {1}~Join~Table[Boole@ PrimePowerQ@ n, {n, 2, 105}] (* Michael De Vlieger, Feb 02 2016 *) PROG (PARI) for(n=1, 120, print1(omega(n)<=1, ", ")) (Haskell) a010055 n = if a001221 n <= 1 then 1 else 0 -- Reinhard Zumkeller, Nov 28 2015, Mar 19 2013, Nov 17 2011 CROSSREFS Cf. A069513 (1 if n is a prime power p^k (k >= 1), else 0.) Cf. A268340. Cf. A100995. Cf. A001221, A000961, A024619, A065515, Sequence in context: A144473 A011750 A340375 * A324290 A325964 A344885 Adjacent sequences: A010052 A010053 A010054 * A010056 A010057 A010058 KEYWORD nonn AUTHOR EXTENSIONS More terms from Charles R Greathouse IV, Mar 12 2008 Edited by Daniel Forgues, Mar 02 2009 Comment re Galois fields moved to A069513 by Franklin T. Adams-Watters, Nov 02 2009 STATUS approved

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Last modified December 9 18:21 EST 2022. Contains 358703 sequences. (Running on oeis4.)