A321874 If n = Product (p_j^k_j) then a(n) = Product (prime(p_j)^prime(k_j)).

1, 9, 25, 27, 121, 225, 289, 243, 125, 1089, 961, 675, 1681, 2601, 3025, 2187, 3481, 1125, 4489, 3267, 7225, 8649, 6889, 6075, 1331, 15129, 3125, 7803, 11881, 27225, 16129, 177147, 24025, 31329, 34969, 3375, 24649, 40401, 42025, 29403, 32041, 65025, 36481, 25947, 15125

Offset: 1

Author

Ilya Gutkovskiy, Nov 20 2018

Keywords

• nonn
• mult

Examples

			a(12) = a(2^2 * 3^1) = prime(2)^prime(2) * prime(3)^prime(1) = 3^3 * 5^2 = 675.
		

Links

• Index entries for sequences computed from indices in prime factorization.

Crossrefs

Cf. A000040, A064988, A304203.

Programs

Mathematica

a[n_] := Times @@ (Prime[#[[1]]]^Prime[#[[2]]] & /@ FactorInteger[n]); a[1] = 1; Table[a[n], {n, 45}]

PARI

a(n) = my(f=factor(n)); prod(k=1, #f~, prime(f[k,1])^prime(f[k,2])); \\ Michel Marcus, Nov 20 2018

PARI

apply( A321874(n)=factorback(apply(prime,factor(n))), [1..49]) \\ M. F. Hasler, Nov 20 2018

Formula

Multiplicative with a(p^e) = prime(p)^prime(e). - M. F. Hasler, Nov 20 2018

Sum_{n>=1} 1/a(n) = Product_{m>=1} (1 + Sum_{k>=1} 1/prime(m)^prime(k)) = 1.22718741... . - Amiram Eldar, Jan 20 2024