A306329 If n = Product (p_j^k_j) then a(n) = Product (p_j)^Sum (k_j).

1, 2, 3, 4, 5, 36, 7, 8, 9, 100, 11, 216, 13, 196, 225, 16, 17, 216, 19, 1000, 441, 484, 23, 1296, 25, 676, 27, 2744, 29, 27000, 31, 32, 1089, 1156, 1225, 1296, 37, 1444, 1521, 10000, 41, 74088, 43, 10648, 3375, 2116, 47, 7776, 49, 1000, 2601, 17576, 53, 1296, 3025, 38416, 3249, 3364, 59, 810000

Offset

1,2

Links

Table of n, a(n) for n=1..60.

Formula

a(n) = rad(n)^bigomega(n) = A007947(n)^A001222(n).

Example

a(12) = a(2^2 * 3^1) = (2 * 3)^(2 + 1) = 216.

Mathematica

Table[Last[Select[Divisors[n], SquareFreeQ]]^PrimeOmega[n], {n, 60}]

Crossrefs

Cf. A000961 (fixed points), A001222, A007947, A088865, A285769, A303277, A303278, A306328.

Sequence in context: A037401 A062509 A061537 * A274029 A056925 A060067

Adjacent sequences: A306326 A306327 A306328 * A306330 A306331 A306332

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 07 2019

Status

approved