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A003599 Numbers of the form 7^i*11^j. 21
1, 7, 11, 49, 77, 121, 343, 539, 847, 1331, 2401, 3773, 5929, 9317, 14641, 16807, 26411, 41503, 65219, 102487, 117649, 161051, 184877, 290521, 456533, 717409, 823543, 1127357, 1294139, 1771561, 2033647, 3195731, 5021863, 5764801 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

FORMULA

The characteristic function of this sequence is given by Sum_{n >= 1} x^a(n) = Sum_{n >= 1} mu(77*n)*x^n/(1 - x^n), where mu(n) is the Möbius function A008683. Cf. with the formula of Hanna in A051037. - Peter Bala, Mar 18 2019

MATHEMATICA

Take[Union[7^#[[1]] 11^#[[2]]&/@Tuples[Range[0, 9], 2]], 40] (* Harvey P. Dale, Mar 11 2015 *)

fQ[n_]:=PowerMod[77, n, n] == 0; Select[Range[6 10^6], fQ] (* Vincenzo Librandi, Jun 27 2016 *)

PROG

(PARI) list(lim)=my(v=List(), N); for(n=0, log(lim)\log(11), N=11^n; while(N<=lim, listput(v, N); N*=7)); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jun 28 2011

(Haskell)

import Data.Set (singleton, deleteFindMin, insert)

a003599 n = a003599_list !! (n-1)

a003599_list = f $ singleton (1, 0, 0) where

   f s = y : f (insert (7 * y, i + 1, j) $ insert (11 * y, i, j + 1) s')

         where ((y, i, j), s') = deleteFindMin s

-- Reinhard Zumkeller, May 15 2015

(MAGMA) [n: n in [1..6*10^6] | PrimeDivisors(n) subset [7, 11]]; // Vincenzo Librandi, Jun 27 2016

CROSSREFS

Cf. A025612, A025616, A025621, A025625, A025629, A025632, A025634, A025635, A108761, A003596, A003597, A107988, A003598, A108698, A107788, A108687, A108779, A108090.

Sequence in context: A105867 A166653 A057290 * A018508 A038277 A045462

Adjacent sequences:  A003596 A003597 A003598 * A003600 A003601 A003602

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified May 22 21:04 EDT 2019. Contains 323500 sequences. (Running on oeis4.)