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A326698 a(n) is the product of divisors d of n such that sigma(d) divides n.

%I A326698 #18 Sep 13 2024 15:57:43
%S A326698 1,1,1,1,1,2,1,1,1,1,1,36,1,1,1,1,1,2,1,1,1,1,1,36,1,1,1,4,1,10,1,1,1,
%T A326698 1,1,36,1,1,1,1,1,2,1,1,1,1,1,36,1,1,1,1,1,2,1,784,1,1,1,180,1,1,1,1,
%U A326698 1,2,1,1,1,1,1,36,1,1,1,1,1,2,1,1,1,1,1
%N A326698 a(n) is the product of divisors d of n such that sigma(d) divides n.
%C A326698 a(A097603(n)) > 1.
%C A326698 See A173441 and A326697 for number and sum such divisors.
%H A326698 Antti Karttunen, <a href="/A326698/b326698.txt">Table of n, a(n) for n = 1..20000</a>
%e A326698 For n = 12, divisors d of 12: 1, 2, 3, 4, 6, 12;
%e A326698 corresponding sigma(d): 1, 3, 4, 7, 12, 28;
%e A326698 sigma(d) divides n for 4 divisors d: 1, 2, 3, 6;
%e A326698 a(12) = 1 * 2 * 3 * 6 = 36.
%t A326698 a[n_] := Times @@ Select[Divisors[n], Divisible[n, DivisorSigma[1, #] &]]; Array[a, 100] (* _Amiram Eldar_, Jul 21 2019 *)
%o A326698 (Magma) [&*[d: d in Divisors(n) | IsIntegral(n / SumOfDivisors(d))]: n in [1..100]];
%o A326698 (PARI) a(n) = my(p=1); fordiv(n, d, if (!(n % sigma(d)), p *= d)); p; \\ _Michel Marcus_, Jul 19 2019
%Y A326698 Cf. A000203, A000961, A173441, A326697.
%K A326698 nonn
%O A326698 1,6
%A A326698 _Jaroslav Krizek_, Jul 19 2019