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A048740 Product of divisors of n-th 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

Albert H. Beiler, Recreations in the Theory of Numbers, 2nd ed., pages 10, 23. New York: Dover, 1966. ISBN 0-486-21096-0.

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)apis-it.hr), May 25 2006

STATUS

approved

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Last modified December 14 01:19 EST 2019. Contains 329978 sequences. (Running on oeis4.)