A152443 a(n) = the largest proper divisor of n that is coprime to d(n), where d(n) = the number of divisors of n.

1, 1, 2, 1, 3, 1, 1, 1, 5, 1, 1, 1, 7, 5, 8, 1, 1, 1, 5, 7, 11, 1, 3, 5, 13, 9, 7, 1, 15, 1, 1, 11, 17, 7, 4, 1, 19, 13, 5, 1, 21, 1, 11, 5, 23, 1, 3, 7, 25, 17, 13, 1, 27, 11, 7, 19, 29, 1, 5, 1, 31, 7, 32, 13, 33, 1, 17, 23, 35, 1, 1, 1, 37, 25, 19, 11, 39, 1, 1, 27, 41, 1, 7, 17, 43, 29, 11, 1, 5

Offset

2,3

Links

Table of n, a(n) for n=2..90.

Example

There are 4 divisors of 27. These are 1,3,9,27. The proper divisors of 27 are therefore 1,3,9. The largest of these that is coprime to d(27) = 4 is 9. So a(27) = 9. (Note that in this case, the largest divisor of 27 coprime to 4 is 27, not 9.)

Mathematica

Table[Max[Select[Drop[Divisors[n], -1], GCD[DivisorSigma[0, n], # ] == 1 &]], {n, 2, 100}] (* Stefan Steinerberger, Dec 06 2008 *)

Crossrefs

Cf. A137926, A152444.

Sequence in context: A328917 A265917 A057021 * A119804 A300977 A144869

Adjacent sequences: A152440 A152441 A152442 * A152444 A152445 A152446

Keyword

nonn

Author

Leroy Quet, Dec 04 2008

Extensions

Extended by Ray Chandler and Stefan Steinerberger, Dec 05 2008

Status

approved