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A048639 Binary encoding of A006881, numbers with two distinct prime divisors. 8

%I #14 Oct 03 2015 03:21:54

%S 3,5,9,6,10,17,33,18,65,12,129,34,257,66,20,130,513,1025,36,258,2049,

%T 24,4097,68,8193,514,40,1026,16385,132,32769,2050,260,65537,72,131073,

%U 4098,8194,136,262145,16386,524289,48,516,1048577,1028,2097153,32770

%N Binary encoding of A006881, numbers with two distinct prime divisors.

%H Michael De Vlieger, <a href="/A048639/b048639.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = 2^(i-1) + 2^(j-1), where A006881(n) = p_i*p_j (p_i and p_j stand for the i-th and j-th primes respectively, where the first prime is 2).

%p encode_A006881 := proc(upto_n) local b,i; b := [ ]; for i from 1 to upto_n do if((0 <> mobius(i)) and (4 = tau(i))) then b := [ op(b), bef(i) ]; fi; od: RETURN(b); end; # see A048623 for bef

%t Total[2^PrimePi@ # &@ (Map[First, FactorInteger@ #] - 1)] & /@ Select[Range@ 160, SquareFreeQ@ # && PrimeOmega@ # == 2 &] (* _Michael De Vlieger_, Oct 01 2015 *)

%o (PARI) lista(nn) = {for (n=1, nn, if (issquarefree(n) && bigomega(n)==2, f = factor(n); x = sum(k=1, #f~, 2^(primepi(f[k,1])-1)); print1(x, ", ");););} \\ _Michel Marcus_, Oct 01 2015

%Y Permutation of A018900. Cf. A048640, A048623.

%K nonn

%O 1,1

%A _Antti Karttunen_, Jul 14 1999

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Last modified April 25 13:12 EDT 2024. Contains 371969 sequences. (Running on oeis4.)