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%I #16 Mar 02 2022 02:09:45
%S 1,3,13,49,47,481,107,6859,3721,3277,257,121841,397,11309,22261,
%T 7890481,653,1390861,881,1416521,78373,47479,1279,157208087,143641,
%U 92011,15813251,7018237,1889,14701639,2293,38579489651,309709,207527,461939,2938615681,3119
%N a(n) = Product p_{n*i}^e_i if the prime factorization of n is Product p_i^e_i.
%C Or replace prime(i) in n by prime(n*i).
%C All terms are odd.
%H Alois P. Heinz, <a href="/A352028/b352028.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A352001(n,n).
%F a(prime(n)) = A228529(n) = A000040(A033286(n)).
%e a(1) = 1 because 1 is the empty product.
%e a(2) = 3 = prime(2) = prime(2*1) because 2 = prime(1).
%e a(3) = 13 = prime(6) = prime(3*2) because 3 = prime(2).
%e a(4) = 49 = 7^2 = prime(4)^2 = prime(4*1)^2 because 4 = prime(1)^2.
%p a:= n-> mul(ithprime(n*numtheory[pi](i[1]))^i[2], i=ifactors(n)[2]):
%p seq(a(n), n=1..45);
%o (PARI) a(n) = my(f=factor(n)); for (k=1, #f~, f[k,1] = prime(n*primepi(f[k,1]))); factorback(f); \\ _Michel Marcus_, Mar 02 2022
%Y Main diagonal of A352001.
%Y Cf A000040, A033286, A228529.
%K nonn
%O 1,2
%A _Alois P. Heinz_, Mar 01 2022
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