A268340 Characteristic function of the prime powers p^k, k >= 2.

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

Offset

1

Comments

Mobius transform of A046660. - Isaac Saffold, Dec 14 2017

Links

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

Formula

a(n) = Sum_{d|n} (mobius(n/d)*(bigomega(d) - omega(d))) - Isaac Saffold, Dec 14 2017

Maple

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

Mathematica

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 *)

Prog

(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
(Python)
from sympy import primefactors
def A268340(n): return int(len(s:=primefactors(n)) == 1 and n>s[0]) # Chai Wah Wu, Mar 31 2023

Crossrefs

Characteristic function of A246547.

Cf. A069513, A010055, A075802, A112526.

Sequence in context: A284508 A347519 A160351 * A355453 A336356 A319988

Adjacent sequences: A268337 A268338 A268339 * A268341 A268342 A268343

Keyword

nonn,easy

Author

Jeppe Stig Nielsen, Feb 02 2016

Extensions

More terms from Antti Karttunen, Nov 03 2017

Status

approved