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

1,1

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).

Links

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

Example

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

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 *)

Crossrefs

Sequence in context: A330184 A008912 A101885 * A045412 A288215 A284625

Adjacent sequences: A096065 A096066 A096067 * A096069 A096070 A096071

Keyword

nonn,base

Author

Reinhard Zumkeller, Jul 21 2004

Status

approved