A352028 a(n) = Product p_{n*i}^e_i if the prime factorization of n is Product p_i^e_i.

1, 3, 13, 49, 47, 481, 107, 6859, 3721, 3277, 257, 121841, 397, 11309, 22261, 7890481, 653, 1390861, 881, 1416521, 78373, 47479, 1279, 157208087, 143641, 92011, 15813251, 7018237, 1889, 14701639, 2293, 38579489651, 309709, 207527, 461939, 2938615681, 3119

Offset: 1

Author

Alois P. Heinz, Mar 01 2022

Keywords

• nonn

Comments

Or replace prime(i) in n by prime(n*i).

All terms are odd.

Examples

			a(1) = 1 because 1 is the empty product.
a(2) = 3 = prime(2) = prime(2*1) because 2 = prime(1).
a(3) = 13 = prime(6) = prime(3*2) because 3 = prime(2).
a(4) = 49 = 7^2 = prime(4)^2 = prime(4*1)^2 because 4 = prime(1)^2.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Main diagonal of A352001.

Cf A000040, A033286, A228529.

Programs

Maple

a:= n-> mul(ithprime(n*numtheory[pi](i[1]))^i[2], i=ifactors(n)[2]):
seq(a(n), n=1..45);

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

Formula

a(n) = A352001(n,n).

a(prime(n)) = A228529(n) = A000040(A033286(n)).