

A048741


Product of aliquot divisors of composite n (1 and primes omitted).


4



2, 6, 8, 3, 10, 144, 14, 15, 64, 324, 400, 21, 22, 13824, 5, 26, 27, 784, 27000, 1024, 33, 34, 35, 279936, 38, 39, 64000, 74088, 1936, 2025, 46, 5308416, 7, 2500, 51, 2704, 157464, 55, 175616, 57, 58, 777600000, 62, 3969, 32768, 65, 287496, 4624, 69
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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) = A007956(A002808(n)).  Michel Marcus, Sep 07 2019


EXAMPLE

The third composite number is 8, for which the product of aliquot divisors is 4*2*1 = 8, so a(3)=8.


MATHEMATICA

Composite[n_] := FixedPoint[n + PrimePi[ # ] + 1 &, n + PrimePi[n] + 1]; Table[ Times @@ Select[ Divisors[ Composite[n]], # < Composite[n] & ], {n, 1, 60} ]
pd[n_] := n^(DivisorSigma[0, n]/2  1); pd /@ Select[Range[100], CompositeQ] (* Amiram Eldar, Sep 07 2019 *)


CROSSREFS

This is A007956 omitting the 1's.
Cf. A002808, A007422, A007956, A048740.
Sequence in context: A119279 A327617 A303495 * A276709 A115317 A117932
Adjacent sequences: A048738 A048739 A048740 * A048742 A048743 A048744


KEYWORD

easy,nonn


AUTHOR

Enoch Haga


EXTENSIONS

a(33) inserted by Amiram Eldar, Sep 07 2019


STATUS

approved



