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A036966 3-full (or cube-full, or cubefull) numbers: if a prime p divides n then so does p^3. 18
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

T. D. Noe, Table of n, a(n) for n = 1..1000

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: A059172 A107606 A245713 * 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

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Last modified May 22 13:18 EDT 2017. Contains 286872 sequences.