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Concatenated in binary representation: largest proper divisor of n and smallest prime factor of n.
1

%I #7 Jul 06 2021 11:05:05

%S 3,6,7,10,13,14,15,18,15,22,27,26,29,30,23,34,49,38,51,42,31,46,55,50,

%T 45,54,39,58,61,62,63,66,47,70,61,74,101,78,55,82,105,86,107,90,63,94,

%U 111,98,63,102,71,106,117,110,93,114,79,118,123,122,125,126,87,130,109

%N Concatenated in binary representation: largest proper divisor of n and smallest prime factor of n.

%C a(n)=A020639(n)*A000079((A000523(A020639(n))+1))+A020639(n);

%C a(A000040(n))=A000079((A000523(A000040(n))+1))+A000040(n);

%C a(A005843(n))=A005843(A005408(n)); a(A000225(n))=A000225(n+1); a(A000079(n))=A052548(n+1).

%H Harvey P. Dale, <a href="/A096068/b096068.txt">Table of n, a(n) for n = 1..1000</a>

%e n=99: smallest factor = 3->'11' and greatest proper divisor =

%e 99/3 = 33->'100001': '10001'&'11'='10000111'->a(99)=135.

%t cbr[n_]:=Module[{sf=FactorInteger[n][[1,1]]},FromDigits[ Join[ IntegerDigits[ n/sf,2],IntegerDigits[sf,2]],2]]; Array[cbr,70] (* _Harvey P. Dale_, Jul 06 2021 *)

%K nonn,base

%O 1,1

%A _Reinhard Zumkeller_, Jul 21 2004