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A010055
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1 if n is a prime power p^k (k >= 0), otherwise 0.
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94
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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FORMULA
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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
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MAPLE
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if n =1 then
1;
else
if nops(ifactors(n)[2]) = 1 then
1;
else
0 ;
end if;
end if;
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MATHEMATICA
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PROG
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(PARI) for(n=1, 120, print1(omega(n)<=1, ", "))
(Haskell)
a010055 n = if a001221 n <= 1 then 1 else 0
(Python)
from sympy import primefactors
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CROSSREFS
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Cf. A069513 (1 if n is a prime power p^k (k >= 1), else 0.)
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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