A072774 Powers of squarefree numbers.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 46, 47, 49, 51, 53, 55, 57, 58, 59, 61, 62, 64, 65, 66, 67, 69, 70, 71, 73, 74, 77, 78, 79, 81, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97

Offset

1,2

Comments

a(n) = A072775(n)^A072776(n); complement of A059404.

Essentially the same as A062770. - R. J. Mathar, Sep 25 2008

Numbers m such that in canonical prime factorization all prime exponents are identical: A124010(m,k) = A124010(m,1) for k = 2..A000005(m). - Reinhard Zumkeller, Apr 06 2014

Heinz numbers of uniform partitions. An integer partition is uniform if all parts appear with the same multiplicity. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). - Gus Wiseman, Apr 16 2018

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Mathematica

Select[Range[100], Length[Union[FactorInteger[#][[All, 2]]]] == 1 &] (* Geoffrey Critzer, Mar 30 2015 *)

Prog

(Haskell)
import Data.Map (empty, findMin, deleteMin, insert)
import qualified Data.Map.Lazy as Map (null)
a072774 n = a072774_list !! (n-1)
(a072774_list, a072775_list, a072776_list) = unzip3 $
   (1, 1, 1) : f (tail a005117_list) empty where
   f vs'@(v:vs) m
    | Map.null m || xx > v = (v, v, 1) :
                             f vs (insert (v^2) (v, 2) m)
    | otherwise = (xx, bx, ex) :
                  f vs' (insert (bx*xx) (bx, ex+1) $ deleteMin m)
    where (xx, (bx, ex)) = findMin m
-- Reinhard Zumkeller, Apr 06 2014
(PARI) is(n)=ispower(n, , &n); issquarefree(n) \\ Charles R Greathouse IV, Oct 16 2015

Crossrefs

Cf. A072777 (subsequence), A005117, A072778, A329332 (tabular arrangement).

A subsequence of A242414.

Cf. A000009, A000837, A007916, A047966, A052409, A052410, A072774, A078374, A289023, A289509, A300486, A302491, A302796, A302979.

Sequence in context: A242414 A360249 A360247 * A062770 A359889 A236510

Adjacent sequences: A072771 A072772 A072773 * A072775 A072776 A072777

Keyword

nonn

Author

Reinhard Zumkeller, Jul 10 2002

Status

approved