

A048740


Product of divisors of nth composite number.


2



8, 36, 64, 27, 100, 1728, 196, 225, 1024, 5832, 8000, 441, 484, 331776, 125, 676, 729, 21952, 810000, 32768, 1089, 1156, 1225, 10077696, 1444, 1521, 2560000, 3111696, 85184, 91125, 2116, 254803968, 343, 125000, 2601, 140608, 8503056, 3025, 9834496
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OFFSET

1,1


REFERENCES

Albert H. Beiler, Recreations in the Theory of Numbers, 2nd ed., pages 10, 23. New York: Dover, 1966. ISBN 0486210960.


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = A007955(A002808(n)).  Michel Marcus, Sep 07 2019


EXAMPLE

The third composite number is 8. The product of all divisors of 8 is 8*4*2*1 = 64.
Divisors(48) = {1,2,3,4,6,8,12,16,24,48} => product {1,2,3,4,6,8,12,16,24,48} = 254803968.
Divisors(49) = {1,7,49} => product {1,7,49} = 343.
Divisors(50) = {1,2,5,10,25,50} => product {1,2,5,10,25,50} = 125000.


MATHEMATICA

Rest[Times@@Divisors[#]&/@Complement[Range[100], Prime[Range[PrimePi[100]]]]] (* Harvey P. Dale, Jan 08 2011 *)
pd[n_] := n^(DivisorSigma[0, n]/2); pd /@ Select[Range[100], CompositeQ] (* Amiram Eldar, Sep 07 2019 *)


CROSSREFS

Cf. A002808, A007955, A048741.
Sequence in context: A200713 A184294 A057345 * A139608 A321778 A009923
Adjacent sequences: A048737 A048738 A048739 * A048741 A048742 A048743


KEYWORD

easy,nonn


AUTHOR

Enoch Haga


EXTENSIONS

Corrected by Neven Juric (neven.juric(AT)apisit.hr), May 25 2006


STATUS

approved



