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A024619
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Numbers that are not powers of primes p^k (k >= 0); complement of A000961.
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32
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6, 10, 12, 14, 15, 18, 20, 21, 22, 24, 26, 28, 30, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100, 102, 104, 105, 106, 108, 110, 111, 112
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Since 1 = p^0 does not have a well defined prime base p it is often excluded from the prime powers, in which case 1 would be prepended to this sequence to give the complement of "Prime powers p^k (k >= 1)". - Daniel Forgues (squid(AT)zensearch.com), Mar 02 2009
The sequence of numbers divisible by a prime number of primes coincides with this up to 210, which has 4 prime factors. - Lior Manor (lior.manor(AT)gmail.com) Aug 23 2001
A085970(n) = Max{k: a(k)<=n}.
Numbers n such that LCM of proper divisors of n equals neither 1 nor n. - Labos E. (labos(AT)ana.sote.hu), Dec 01 2004
A010055(a(n)) = 0. [Reinhard Zumkeller, Nov 17 2011]
a(n) provides bases b in which automorphic numbers m^2 ending with m in base b exist. In the complement there aren't any automorphic numbers. - Martin Renner, Dec 07 2011
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LINKS
| Daniel Forgues (upto n=8719) and Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Prime Power
Wikipedia, Prime power
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FORMULA
| A001221(a(n)) > 1.
A014963(a(n)) = 1.
A020500(a(n)) = 1 - Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 26 2003
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MAPLE
| Contribution from Peter Luschny (peter(AT)luschny.de), Aug 11 2009: (Start)
a := proc(n) numtheory[factorset](n); if 1 < nops(%) then n else NULL fi end:
seq(a(i), i=1..110); (End)
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MATHEMATICA
| Select[Range@111, Length@FactorInteger@# > 1 &] (from Robert G. Wilson v (rgwv(at)rgwv.com), Dec 07 2005)
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PROG
| (MAGMA) IsA024619:=func< n | not IsPrime(n) and not (t and IsPrime(b) where t, b, _:=IsPower(n)) >; [ n: n in [2..200] | IsA024619(n) ]; // Klaus Brockhaus, Feb 25 2011
(Haskell)
a024619 n = a024619_list !! (n-1)
a024619_list = filter ((== 0) . a010055) [1..]
-- Reinhard Zumkeller, Nov 17 2011
(Sage)
def A024619_list(n) :
return [k for k in (1..n) if not k.is_prime() and not k.is_perfect_power()]
A024619_list(112) # Peter Luschny, Feb 03 2012
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CROSSREFS
| Cf. A000040, A000961, A001221, A014963, A020500, A085970.
Sequence in context: A105642 A064040 A168638 * A106543 A007774 A030231
Adjacent sequences: A024616 A024617 A024618 * A024620 A024621 A024622
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KEYWORD
| nonn,changed
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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