A048741 - OEIS

A048741

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

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

(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) = 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: A344171 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