A072505 a(n) = n / (LCM of divisors of n which are <= sqrt(n)).

1, 2, 3, 2, 5, 3, 7, 4, 3, 5, 11, 2, 13, 7, 5, 4, 17, 3, 19, 5, 7, 11, 23, 2, 5, 13, 9, 7, 29, 1, 31, 8, 11, 17, 7, 3, 37, 19, 13, 2, 41, 7, 43, 11, 3, 23, 47, 4, 7, 5, 17, 13, 53, 9, 11, 2, 19, 29, 59, 1, 61, 31, 3, 8, 13, 11, 67, 17, 23, 1, 71, 3, 73, 37, 5, 19, 11, 13, 79, 2, 9, 41, 83

Offset

1,2

Links

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

Formula

From Robert Israel, Mar 19 2018: (Start)

If n = p^k for prime p, then a(n) = p^ceiling(k/2).

In particular, a(n) = n if and only if n is prime.

If n = p*q for primes p < q, then a(n) = q. (End)

Example

a(20) = 5: the divisors of 20 are 1,2,4,5,10 and 20; a(20) = 20/lcm(1,2,4) = 20/4 = 5.

Maple

f:= proc(n) n/ilcm(op(select(t -> t^2 <= n, numtheory:-divisors(n)))) end proc:
map(f, [$1..100]); # Robert Israel, Mar 19 2018

Mathematica

lc[n_]:=Module[{c=Select[Divisors[n], #<=Sqrt[n]&]}, n/LCM@@c]; Array[lc, 90] (* Harvey P. Dale, May 18 2012 *)

Crossrefs

Cf. A072504.

Sequence in context: A219964 A165500 A341679 * A095163 A033677 A116548

Adjacent sequences: A072502 A072503 A072504 * A072506 A072507 A072508

Keyword

nonn,look

Author

Amarnath Murthy, Jul 20 2002

Extensions

Corrected and extended by Matthew Conroy, Sep 09 2002

Status

approved