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%I #15 Sep 10 2017 11:35:25
%S 1,3,4,21,6,144,8,315,52,324,12,28224,14,576,576,9765,18,73008,20,
%T 95256,1024,1296,24,25401600,186,1764,2080,225792,30,26873856,32,
%U 615195,2304,2916,2304,1302170688,38,3600,3136,128595600,42,84934656,44,762048,584064
%N a(n) = product of numbers k <= sigma(n) such that k = sigma(d) for any divisor d of n where sigma = A000203.
%C Sequence is not the same as A206032(n): a(66) = 35831808, A206032(66) = 429981696.
%C In sequence A206032 are multiplied all values of sigma(d) of all divisors d of numbers n, in sequence a(n) are multiplied only distinct values of sigma(d) of all divisors d of numbers n.
%H Antti Karttunen, <a href="/A206031/b206031.txt">Table of n, a(n) for n = 1..4096</a>
%F a(p) = p+1, a(pq) = ((p+1)*(q+1))^2 for p, q = distinct primes.
%e For n=6 -> divisors d of 6: 1,2,3,6; corresponding values of sigma(d): 1,3,4,12; a(6) = Product of k = 1*3*4*12 = 144. For n=66 -> divisors d of 66: 1,2,3,6,11,22,33,66; corresponding values of sigma(d): 1,3,4,12,12,36,48,144; a(66) = Product of k = 1*3*4*12*36*48*144 = 35831808.
%t Table[Times @@ Union[DivisorSigma[1, Divisors[n]]], {n, 100}] (* _T. D. Noe_, Feb 10 2012 *)
%o (PARI) a(n)=my(d=vecsort(apply(sigma,divisors(n)),,8));prod(i=2,#d,d[i]) \\ _Charles R Greathouse IV_, Feb 19 2013
%Y Cf. A184388, A184395, A206032, A206033.
%K nonn
%O 1,2
%A _Jaroslav Krizek_, Feb 03 2012