A003599 Numbers of the form 7^i*11^j.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

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

Crossrefs

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

Programs

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

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 *)

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

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

Sum_{n>=1} 1/a(n) = (7*11)/((7-1)*(11-1)) = 77/60. - Amiram Eldar, Sep 23 2020

a(n) ~ exp(sqrt(2*log(7)*log(11)*n)) / sqrt(77). - Vaclav Kotesovec, Sep 23 2020