cp's OEIS Frontend

A329352 a(n) = Product_{d|n} A019565(d)^A010051(n/d).

%I A329352 #7 Nov 12 2019 19:20:21
%S A329352 1,2,2,3,2,18,2,5,6,30,2,75,2,90,60,7,2,210,2,105,180,126,2,245,10,
%T A329352 210,14,525,2,66150,2,11,252,66,300,1155,2,198,420,385,2,173250,2,825,
%U A329352 2940,990,2,847,30,3234,132,1155,2,15246,420,2695,396,2310,2,2223375,2,6930,1540,13,700,64350,2,195,1980,171990,2,5005,2,390,32340,975,1260
%N A329352 a(n) = Product_{d|n} A019565(d)^A010051(n/d).
%H A329352 Antti Karttunen, <a href="/A329352/b329352.txt">Table of n, a(n) for n = 1..8192</a>
%F A329352 a(n) = Product_{d|n} A019565(d)^A010051(n/d).
%F A329352 For all n, A048675(a(n)) = A069359(n).
%e A329352 The divisors of 30 are [1, 2, 3, 5, 6, 10, 15, 30], of which only d = 6, 10 and 15 are such that 30/d is a prime, thus a(n) = A019565(6) * A019565(10) * A019565(15) = 15 * 21 * 210 = 66150.
%o A329352 (PARI)
%o A329352 A019565(n) = {my(j,v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ From A019565
%o A329352 A329352(n) = { my(m=1); fordiv(n,d,if(isprime(n/d), m *= A019565(d))); (m); };
%Y A329352 Cf. A010051, A019565, A048675, A069359, A329353 (rgs-transform).
%Y A329352 Cf. also A329350.
%Y A329352 Differs from A300832 for the first time at n=30, where a(30) = 66150, while A300832(30) = 132300.
%K A329352 nonn
%O A329352 1,2
%A A329352 _Antti Karttunen_, Nov 12 2019