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A061538 Product of all divisors of n, divided by product of unitary divisors; or equivalently product of non-unitary divisors of n. 5
1, 1, 1, 2, 1, 1, 1, 8, 3, 1, 1, 12, 1, 1, 1, 64, 1, 18, 1, 20, 1, 1, 1, 576, 5, 1, 27, 28, 1, 1, 1, 1024, 1, 1, 1, 7776, 1, 1, 1, 1600, 1, 1, 1, 44, 45, 1, 1, 110592, 7, 50, 1, 52, 1, 2916, 1, 3136, 1, 1, 1, 3600, 1, 1, 63, 32768, 1, 1, 1, 68, 1, 1, 1, 26873856, 1, 1, 75, 76, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = n^(A048105(n)/2) = n^((A000005(n) - A034444(n))/2).

EXAMPLE

n=16: only {1,16} are unitary, while {2,4,8} are non-unitary divisors, so a(16)=64. When all divisors are unitary, then A048105 is 0 and corresponding terms here are equal to 1.

MATHEMATICA

Table[Times @@ Select[Divisors@ n, ! CoprimeQ[#, n/#] &], {n, 79}] (* Michael De Vlieger, Mar 17 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("b061538.txt", n, " ", a) ) } \\ Harry J. Smith, Jul 24 2009

CROSSREFS

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

Sequence in context: A157117 A322143 A264081 * A123602 A208896 A288972

Adjacent sequences:  A061535 A061536 A061537 * A061539 A061540 A061541

KEYWORD

nonn

AUTHOR

Labos Elemer, May 15 2001

EXTENSIONS

Corrected and edited by Jaroslav Krizek, Mar 05 2009

STATUS

approved

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Last modified September 21 02:23 EDT 2020. Contains 337266 sequences. (Running on oeis4.)