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
Offset: 1
Examples
The third composite number is 8, for which the product of aliquot divisors is 4*2*1 = 8, so a(3)=8.
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
Programs
-
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 *)
Formula
Extensions
a(33) inserted by Amiram Eldar, Sep 07 2019