login
This site is supported by donations to The OEIS Foundation.

 

Logo

"Email this user" was broken Aug 14 to 9am Aug 16. If you sent someone a message in this period, please send it again.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A024619 Numbers that are not powers of primes p^k (k >= 0); complement of A000961. 59
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; text; internal format)
OFFSET

1,1

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, 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 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 Elemer, 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

Numbers with at least 2 distinct prime factors. - Jonathan Sondow, Oct 17 2013

There exists an equiangular n-gon 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

LINKS

Daniel Forgues and Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 (first 8719 terms from Daniel Forgues)

Marius Munteanu and Laura Munteanu, Rational equiangular polygons, Applied Math., 4 (2013), 1460-1465.

Eric Weisstein's World of Mathematics, Prime Power

Wikipedia, Prime power

G. J. Woeginger, Nothing new about equiangular polygons, Amer. Math. Monthly, 120 (2013), 849-850.

FORMULA

A001221(a(n)) > 1.

A014963(a(n)) = 1.

A020500(a(n)) = 1 - Benoit Cloitre, Aug 26 2003

a(n) ~ n. - Charles R Greathouse IV, Mar 21 2013

A118887(a(n)) > 0. - Jonathan Sondow, Oct 17 2013

MAPLE

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

seq(a(i), i=1..110); # Peter Luschny, Aug 11 2009

MATHEMATICA

Select[Range@111, Length@FactorInteger@# > 1 &] (* Robert G. Wilson v, Dec 07 2005 *)

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

(PARI) is(n)=n>5 && !isprimepower(n) \\ Charles R Greathouse IV, Mar 21 2013

CROSSREFS

Cf. A000040, A000961, A001221, A014963, A020500, A085970.

Subsequence of A080257.

Sequence in context: A105642 A064040 A168638 * A106543 A007774 A030231

Adjacent sequences:  A024616 A024617 A024618 * A024620 A024621 A024622

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified August 21 17:48 EDT 2017. Contains 290892 sequences.