Search: id:A064547
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%I A064547
%S A064547 0,1,1,1,1,2,1,2,1,2,1,2,1,2,2,1,1,2,1,2,2,2,1,3,1,2,2,2,1,3,1,2,2,2,2,
%T A064547 2,1,2,2,3,1,3,1,2,2,2,1,2,1,2,2,2,1,3,2,3,2,2,1,3,1,2,2,2,2,3,1,2,2,3,
%U A064547 1,3,1,2,2,2,2,3,1,2,1,2,1,3,2,2,2,3,1,3,2,2,2,2,2,3,1,2,2,2,1,3,1,3,3
%N A064547 Sum of binary digits (or count of 1-bits) in the exponents of the prime 
               factorization of n.
%C A064547 This sequence is different from A058061 for n containing 6th, 8th, ..., 
               k-th powers in its prime decomposition, where k runs through the 
               integers missing from A064548.
%C A064547 For n > 1, n is a product of a(n) distinct members of A050376. - Matthew 
               Vandermast (ghodges14(AT)comcast.net), Jul 13 2004
%H A064547 Harry J. Smith, <a href="b064547.txt">Table of n, a(n) for n=1,...,2000</
               a>
%e A064547 a(54)=3 since 54=2^1 * 3^3 with exponents (1) and (11) in binary
%p A064547 Maple program from N. J. A. Sloane (njas(AT)research.att.com), Dec 20 
               2007:
%p A064547 expts:=proc(n) local t1,t2,t3,t4,i; if n=1 then RETURN([0]); fi; if isprime(n) 
               then RETURN([1]); fi; t1:=ifactor(n); if nops(factorset(n))=1 then 
               RETURN([op(2,t1)]); fi; t2:=nops(t1); t3:=[]; for i from 1 to t2 
               do t4:=op(i,t1); if nops(t4) = 1 then t3:=[op(t3),1]; else t3:=[op(t3),
               op(2,t4)]; fi; od; RETURN(t3); end;
%p A064547 A000120 := proc(n) local w,m,i; w := 0; m := n; while m > 0 do i := m 
               mod 2; w := w+i; m := (m-i)/2; od; w; end:
%p A064547 LamMos:= proc(n) local t1,t2,t3,i; t1:=expts(n); add( A000120(t1[i]),
               i=1..nops(t1)); end;
%t A064547 Table[Plus@@(DigitCount[Last/@FactorInteger[k], 2, 1]), {k, 105}]
%o A064547 (PARI) SumD(x)= { local(s); s=0; while (x>9, s+=x-10*(x\10); x\=10); 
               return(s + x) } baseE(x, b)= { local(d,e,f); e=0; f=1; while (x>0, 
               d=x-b*(x\b); x\=b; e+=d*f; f*=10); return(e) } { for (n=1, 2000, 
               f=factor(n)~; a=0; for (i=1, length(f), a+=SumD(baseE(f[2, i], 2))); 
               write("b064547.txt", n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               Sep 18 2009]
%Y A064547 Cf. A000028, A000379, A058061.
%Y A064547 Sequence in context: A160980 A065031 A058061 this_sequence A086435 A099305 
               A033109
%Y A064547 Adjacent sequences: A064544 A064545 A064546 this_sequence A064548 A064549 
               A064550
%K A064547 nonn
%O A064547 1,6
%A A064547 Wouter Meeussen (wouter.meeussen(AT)pandora.be), Oct 09 2001

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