A096068 Concatenated in binary representation: largest proper divisor of n and smallest prime factor of n.

3, 6, 7, 10, 13, 14, 15, 18, 15, 22, 27, 26, 29, 30, 23, 34, 49, 38, 51, 42, 31, 46, 55, 50, 45, 54, 39, 58, 61, 62, 63, 66, 47, 70, 61, 74, 101, 78, 55, 82, 105, 86, 107, 90, 63, 94, 111, 98, 63, 102, 71, 106, 117, 110, 93, 114, 79, 118, 123, 122, 125, 126, 87, 130, 109

Offset: 1

Author

Reinhard Zumkeller, Jul 21 2004

Keywords

• nonn
• base

Comments

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

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

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

Examples

			n=99: smallest factor = 3->'11' and greatest proper divisor =
99/3 = 33->'100001': '10001'&'11'='10000111'->a(99)=135.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Programs

Mathematica

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 *)