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A048741 Product of aliquot divisors of composite n (1 and primes omitted). 4

%I #12 Sep 07 2019 08:49:25

%S 2,6,8,3,10,144,14,15,64,324,400,21,22,13824,5,26,27,784,27000,1024,

%T 33,34,35,279936,38,39,64000,74088,1936,2025,46,5308416,7,2500,51,

%U 2704,157464,55,175616,57,58,777600000,62,3969,32768,65,287496,4624,69

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

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

%H Amiram Eldar, <a href="/A048741/b048741.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A007956(A002808(n)). - _Michel Marcus_, Sep 07 2019

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

%t Composite[n_] := FixedPoint[n + PrimePi[ # ] + 1 &, n + PrimePi[n] + 1]; Table[ Times @@ Select[ Divisors[ Composite[n]], # < Composite[n] & ], {n, 1, 60} ]

%t pd[n_] := n^(DivisorSigma[0, n]/2 - 1); pd /@ Select[Range[100], CompositeQ] (* _Amiram Eldar_, Sep 07 2019 *)

%Y This is A007956 omitting the 1's.

%Y Cf. A002808, A007422, A007956, A048740.

%K easy,nonn

%O 1,1

%A _Enoch Haga_

%E a(33) inserted by _Amiram Eldar_, Sep 07 2019

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Last modified May 12 18:22 EDT 2024. Contains 372494 sequences. (Running on oeis4.)