

A024619


Numbers that are not powers of primes p^k (k >= 0); complement of A000961.


135



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
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OFFSET

1,1


COMMENTS

The sequence of numbers divisible by a prime number of primes coincides with this up to 210, which has 4 prime factors.  Lior Manor Aug 23 2001
Numbers n such that LCM of proper divisors of n equals neither 1 nor n.  Labos Elemer, Dec 01 2004
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
Numbers with at least 2 distinct prime factors.  Jonathan Sondow, Oct 17 2013
There exists an equiangular ngon whose edge lengths form a permutation of 1, 2, ..., n if and only if n is in the sequence (see Woeginger's survey and Munteanu & Munteanu).  Jonathan Sondow, Oct 17 2013
Numbers that are the product of two relatively prime factors. These numbers are used in testing a sequence for multiplicativity.  Michael Somos, Jun 02 2015
A theorem from Donald McCarthy: Let d be any positive integer which is not a prime power; then there exists a finite group whose order is divisible by d but which contains no subgroup of order d (see link and A340511).  Bernard Schott, Dec 04 2021


LINKS



FORMULA



MAPLE

a := proc(n) numtheory[factorset](n); if 1 < nops(%) then n else NULL fi end:


MATHEMATICA



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 !! (n1)
a024619_list = filter ((== 0) . a010055) [1..]
(Sage)
return [k for k in (2..n) if not k.is_prime() and not k.is_prime_power()]


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



