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A268340
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Characteristic function of the prime powers p^k, k >= 2.
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4
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0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1
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COMMENTS
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Mobius transform of A046660. - Isaac Saffold, Dec 14 2017
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LINKS
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Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for characteristic functions
Index entries for sequences computed from exponents in factorization of n
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FORMULA
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a(n) = Sum_{d|n} (mobius(n/d)*(bigomega(d) - omega(d))) - Isaac Saffold, Dec 14 2017
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MAPLE
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N:= 1000: # to get a(1)...a(N)
V:= Vector(N):
for p in select(isprime, [2, seq(i, i=3..isqrt(N), 2)]) do
for k from 2 to floor(log[p](N)) do
V[p^k]:= 1
od od:
convert(V, list); # Robert Israel, Dec 14 2017
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MATHEMATICA
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Table[Boole@ And[PrimePowerQ@ n, ! PrimeQ@ n], {n, 105}] (* Michael De Vlieger, Feb 02 2016 *)
Table[If[!PrimeQ[n]&&PrimePowerQ[n], 1, 0], {n, 130}] (* Harvey P. Dale, Jan 20 2019 *)
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PROG
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(PARI) a(n)=my(b); ispower(n, , &b)&&isprime(b)
(PARI) first(n) = my(res = vector(n)); forprime(p = 2, sqrtint(n), for(i = 2, logint(n, p), res[p^i] = 1)); res \\ David A. Corneth, Nov 03 2017
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CROSSREFS
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Characteristic function of A246547.
Cf. A069513, A010055, A075802, A112526.
Sequence in context: A283316 A284508 A160351 * A336356 A319988 A023969
Adjacent sequences: A268337 A268338 A268339 * A268341 A268342 A268343
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KEYWORD
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nonn,easy
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AUTHOR
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Jeppe Stig Nielsen, Feb 02 2016
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EXTENSIONS
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More terms from Antti Karttunen, Nov 03 2017
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STATUS
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approved
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