Search: id:A048675
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%I A048675
%S A048675 0,1,2,2,4,3,8,3,4,5,16,4,32,9,6,4,64,5,128,6,10,17,256,5,8,33,6,10,
%T A048675 512,7,1024,5,18,65,12,6,2048,129,34,7,4096,11,8192,18,8,257,16384,6,
%U A048675 16,9,66,34,32768,7,20,11,130,513,65536,8,131072,1025,12,6,36,19
%N A048675 Binary encoding of factorizations, a(n) = bef(n).
%C A048675 Gives bijective mapping if the source sequence is square-free (A048672), 
               or there are max two prime divisors or one p with max exponent being 
               2 (A048623 and A048639).
%F A048675 a(1) = 0, a(n) = 1/2 * (e1*2^i1 + e2*2^i2 + ... + ez*2^iz) if n = p_i1^e1*p_i2^e2*...*p_iz^ez, 
               where p_i isi-th prime. (e.g. p1=2, p2=3)
%F A048675 Totally additive with a(p^e) = 2^(PrimePi(p)-1), where PrimePi(n) = A000720(n).
%p A048675 nthprime := proc(n) local i; if(isprime(n)) then for i from 1 to 1000000 
               do if(ithprime(i) = n) then RETURN(i); fi; od; else RETURN(0); fi; 
               end; # nthprime(2) = 1, nthprime(3) = 2, nthprime(5) = 3, etc. - 
               this is also A049084.
%p A048675 A048675 := proc(n) local s,d; s := 0; for d in ifactors(n)[ 2 ] do s 
               := s + d[ 2 ]*(2^(nthprime(d[ 1 ])-1)); od; RETURN(s); end; bef := 
               A048675; # bef = Binary Encode Factorization.
%Y A048675 Cf. A048623, A048676.
%Y A048675 Sequence in context: A096441 A100824 A163227 this_sequence A162474 A048676 
               A049287
%Y A048675 Adjacent sequences: A048672 A048673 A048674 this_sequence A048676 A048677 
               A048678
%K A048675 nonn
%O A048675 1,3
%A A048675 Antti Karttunen, Jul 14 1999

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