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A157721 a(n) = 0 if n is 1 or a prime, otherwise a(n) = product of composite (nonprime) divisors of n.

%I A157721 #11 Aug 01 2024 01:33:52
%S A157721 0,0,0,4,0,6,0,32,9,10,0,288,0,14,15,512,0,972,0,800,21,22,0,55296,25,
%T A157721 26,243,1568,0,27000,0,16384,33,34,35,1679616,0,38,39,256000,0,74088,
%U A157721 0,3872,6075,46,0,42467328,49,12500,51,5408,0,1417176,55,702464,57,58,0
%N A157721 a(n) = 0 if n is 1 or a prime, otherwise a(n) = product of composite (nonprime) divisors of n.
%C A157721 a(n) = 0 if n = 1 or n is prime; a(n) = n if n is semiprime (A001358). a(c) = A007955(c) / A007947(c) = (c^(A000005(c)/2)) / A007947(c) = A087652(c), for c = composite numbers (A002808). a(p) = A087652(p) - 1 = 0, for p = primes (A000040).
%H A157721 Robert Israel, <a href="/A157721/b157721.txt">Table of n, a(n) for n = 1..10000</a>
%e A157721 a(12) = 4*6*12 = 288, composite divisors = {4,6,12}.
%p A157721 f:= proc(n) if isprime(n) then 0 else convert(remove(isprime,numtheory:-divisors(n)),`*`) fi end proc;
%p A157721 f(1):= 0:
%p A157721 map(f, [$1..100]); # _Robert Israel_, Jul 31 2024
%t A157721 f[n_] := If[n == 1 || PrimeQ@n, 0, Times @@ Select[Divisors@n, ! PrimeQ@# &]]; Array[f, 60] (* _Robert G. Wilson v_, May 04 2009 *)
%Y A157721 Cf. A007955, A007947, A000005, A087652, A002808, A000040.
%K A157721 nonn,look
%O A157721 1,4
%A A157721 _Jaroslav Krizek_, Mar 04 2009
%E A157721 More terms from _Robert G. Wilson v_, May 04 2009