A137926 a(n) = the largest divisor of n that is coprime to A000005(n). (A000005(n) = the number of positive divisors of n.)

1, 1, 3, 4, 5, 3, 7, 1, 1, 5, 11, 1, 13, 7, 15, 16, 17, 1, 19, 5, 21, 11, 23, 3, 25, 13, 27, 7, 29, 15, 31, 1, 33, 17, 35, 4, 37, 19, 39, 5, 41, 21, 43, 11, 5, 23, 47, 3, 49, 25, 51, 13, 53, 27, 55, 7, 57, 29, 59, 5, 61, 31, 7, 64, 65, 33, 67, 17, 69, 35, 71, 1, 73, 37, 25, 19, 77, 39, 79

Offset

1,3

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

6 has 4 positive divisors. The divisors of 6 are 1,2,3,6. The divisors of 6 that are coprime to 4 are 1 and 3. 3 is the largest of these; so a(6) = 3.

Maple

f := proc (n) local D, t; D := numtheory:-divisors(n); t := nops(D); max(select(proc (d) options operator, arrow; igcd(d, t) = 1 end proc, D)) end proc:
map(f, [$1..100]); # Robert Israel, Feb 11 2018

Mathematica

Table[Select[Divisors[n], GCD[ #, Length[Divisors[n]]] == 1 &][[ -1]], {n, 1, 80}] (* Stefan Steinerberger, Mar 09 2008 *)

Prog

(PARI) a(n) = {my(d = divisors(n)); vecmax(select(x->(gcd(x, #d) == 1), d)); } \\ Michel Marcus, Feb 12 2018

Crossrefs

Cf. A046642 (a(n)=n), A120737 (a(n)=1), A137927.

Sequence in context: A178231 A343262 A298734 * A218342 A090395 A168485

Adjacent sequences: A137923 A137924 A137925 * A137927 A137928 A137929

Keyword

nonn

Author

Leroy Quet, Feb 23 2008

Extensions

More terms from Stefan Steinerberger, Mar 09 2008

Status

approved