

A137926


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


4



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
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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: A121890 A178231 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



