cp's OEIS Frontend

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

%I A003599 #31 Oct 22 2023 16:26:05
%S A003599 1,7,11,49,77,121,343,539,847,1331,2401,3773,5929,9317,14641,16807,
%T A003599 26411,41503,65219,102487,117649,161051,184877,290521,456533,717409,
%U A003599 823543,1127357,1294139,1771561,2033647,3195731,5021863,5764801
%N A003599 Numbers of the form 7^i*11^j.
%H A003599 Reinhard Zumkeller, <a href="/A003599/b003599.txt">Table of n, a(n) for n = 1..10000</a>
%F A003599 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
%F A003599 Sum_{n>=1} 1/a(n) = (7*11)/((7-1)*(11-1)) = 77/60. - _Amiram Eldar_, Sep 23 2020
%F A003599 a(n) ~ exp(sqrt(2*log(7)*log(11)*n)) / sqrt(77). - _Vaclav Kotesovec_, Sep 23 2020
%t A003599 Take[Union[7^#[[1]] 11^#[[2]]&/@Tuples[Range[0,9],2]],40] (* _Harvey P. Dale_, Mar 11 2015 *)
%t A003599 fQ[n_]:=PowerMod[77, n, n] == 0; Select[Range[6 10^6], fQ] (* _Vincenzo Librandi_, Jun 27 2016 *)
%o A003599 (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
%o A003599 (Haskell)
%o A003599 import Data.Set (singleton, deleteFindMin, insert)
%o A003599 a003599 n = a003599_list !! (n-1)
%o A003599 a003599_list = f $ singleton (1,0,0) where
%o A003599    f s = y : f (insert (7 * y, i + 1, j) $ insert (11 * y, i, j + 1) s')
%o A003599          where ((y, i, j), s') = deleteFindMin s
%o A003599 -- _Reinhard Zumkeller_, May 15 2015
%o A003599 (Magma) [n: n in [1..6*10^6] | PrimeDivisors(n) subset [7, 11]]; // _Vincenzo Librandi_, Jun 27 2016
%Y A003599 Cf. A025612, A025616, A025621, A025625, A025629, A025632, A025634, A025635, A108761, A003596, A003597, A107988, A003598, A108698, A107788, A108687, A108779, A108090.
%K A003599 nonn,easy
%O A003599 1,2
%A A003599 _N. J. A. Sloane_