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

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A036966 3-full (or cube-full, or cubefull) numbers: if a prime p divides n then so does p^3. 21
1, 8, 16, 27, 32, 64, 81, 125, 128, 216, 243, 256, 343, 432, 512, 625, 648, 729, 864, 1000, 1024, 1296, 1331, 1728, 1944, 2000, 2048, 2187, 2197, 2401, 2592, 2744, 3125, 3375, 3456, 3888, 4000, 4096, 4913, 5000, 5184, 5488, 5832, 6561, 6859, 6912, 7776, 8000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also called powerful_3 numbers.

For n > 1: A124010(a(n),k) > 2, k = 1..A001221(a(n)). - Reinhard Zumkeller, Dec 15 2013

a(m) mod prime(n) > 0 for m < A258600(n); a(A258600(n)) = A030078(n) = prime(n)^3. - Reinhard Zumkeller, Jun 06 2015

REFERENCES

M. J. Halm, More Sequences, Mpossibilities 83, April 2003.

A. Ivic, The Riemann Zeta-Function, Wiley, NY, 1985, see p. 407.

E. Kraetzel, Lattice Points, Kluwer, Chap. 7, p. 276.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)

P. Erdős and G. Szekeres, Über die Anzahl der Abelschen Gruppen gegebener Ordnung und über ein verwandtes zahlentheoretisches Problem, Acta Sci. Math. (Szeged), 7 (1935), 95-102.

M. J. Halm, Sequences

Index entries for sequences related to powerful numbers

MAPLE

isA036966 := proc(n)

    local p ;

    for p in ifactors(n)[2] do

        if op(2, p) < 3 then

            return false;

        end if;

    end do:

    return true ;

end proc:

A036966 := proc(n)

    option remember;

    if n = 1 then

        1 ;

    else

        for a from procname(n-1)+1 do

            if isA036966(a) then

                return a;

            end if;

        end do:

    end if;

end proc: # R. J. Mathar, May 01 2013

MATHEMATICA

Select[ Range[2, 8191], Min[ Table[ # [[2]], {1}] & /@ FactorInteger[ # ]] > 2 &]

Join[{1}, Select[Range[8000], Min[Transpose[FactorInteger[#]][[2]]]>2&]] (* Harvey P. Dale, Jul 17 2013 *)

PROG

(Haskell)

import Data.Set (singleton, deleteFindMin, fromList, union)

a036966 n = a036966_list !! (n-1)

a036966_list = 1 : f (singleton z) [1, z] zs where

   f s q3s p3s'@(p3:p3s)

     | m < p3 = m : f (union (fromList $ map (* m) ps) s') q3s p3s'

     | otherwise = f (union (fromList $ map (* p3) q3s) s) (p3:q3s) p3s

     where ps = a027748_row m

           (m, s') = deleteFindMin s

   (z:zs) = a030078_list

-- Reinhard Zumkeller, Jun 03 2015, Dec 15 2013

(PARI) is(n)=n==1 || vecmin(factor(n)[, 2])>2 \\ Charles R Greathouse IV, Sep 17 2015

(PARI) list(lim)=my(v=List(), t); for(a=1, sqrtnint(lim\1, 5), for(b=1, sqrtnint(lim\a^5, 4), t=a^5*b^4; for(c=1, sqrtnint(lim\t, 3), listput(v, t*c^3)))); Set(v) \\ Charles R Greathouse IV, Nov 20 2015

CROSSREFS

Cf. A001694, A030078, A036967, A258600.

Sequence in context: A107606 A245713 A320966 * A076467 A111231 A111307

Adjacent sequences:  A036963 A036964 A036965 * A036967 A036968 A036969

KEYWORD

easy,nonn,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Erich Friedman

Corrected by Vladeta Jovovic, Aug 17 2002

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 8 17:36 EST 2019. Contains 329865 sequences. (Running on oeis4.)