A061537 Product of unitary divisors of n.

1, 2, 3, 4, 5, 36, 7, 8, 9, 100, 11, 144, 13, 196, 225, 16, 17, 324, 19, 400, 441, 484, 23, 576, 25, 676, 27, 784, 29, 810000, 31, 32, 1089, 1156, 1225, 1296, 37, 1444, 1521, 1600, 41, 3111696, 43, 1936, 2025, 2116, 47, 2304, 49, 2500, 2601, 2704, 53, 2916

Offset

1,2

Comments

Also appears to be smallest number m such that A066296(m) = n.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..20000 (terms n=1..1000 from Harry J. Smith)

Formula

a(n) = n^(A034444(n)/2) = n^(2^(A001221(n)-1).

Example

n = 288, unitary divisors = {1,9,32,288}, a(288) = 82944

Maple

a:= n-> mul(`if`(igcd(d, n/d)=1, d, 1), d=numtheory[divisors](n)):
seq(a(n), n=1..30);  # Alois P. Heinz, Aug 01 2017

Mathematica

Table[Times@@ Select[Divisors[n], GCD[#, n/#]==1 &], {n, 1, 100}] (* Indranil Ghosh, Aug 04 2017 *)

Prog

(PARI) { for (n=1, 1000, s=divisors(n); a=1; for (i=2, length(s), d=s[i]; if (gcd(d, n/d)==1, a*=d)); write("b061537.txt", n, " ", a) ) } \\ Harry J. Smith, Jul 24 2009
(Python)
from sympy import divisors, gcd, prod
def a(n): return prod(d for d in divisors(n) if gcd(d, n//d)==1)
print([a(n) for n in range(1, 51)]) # Indranil Ghosh, Aug 04 2017

Crossrefs

Cf. A000005, A001221, A007955, A007956, A034444, A048105, A066296.

Sequence in context: A286902 A037401 A062509 * A306329 A274029 A056925

Adjacent sequences: A061534 A061535 A061536 * A061538 A061539 A061540

Keyword

nonn

Author

Labos Elemer, May 15 2001

Extensions

Corrected and edited by Jaroslav Krizek, Mar 05 2009

Status

approved