A381588 If n = Product (p_j^k_j) then a(n) = Product (lcm(p_j, k_j)), with a(1) = 1.

1, 2, 3, 2, 5, 6, 7, 6, 6, 10, 11, 6, 13, 14, 15, 4, 17, 12, 19, 10, 21, 22, 23, 18, 10, 26, 3, 14, 29, 30, 31, 10, 33, 34, 35, 12, 37, 38, 39, 30, 41, 42, 43, 22, 30, 46, 47, 12, 14, 20, 51, 26, 53, 6, 55, 42, 57, 58, 59, 30, 61, 62, 42, 6, 65, 66, 67, 34, 69, 70, 71

Offset

1,2

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Formula

a(p) = p, for p prime.

Example

a(18) = 12 because 18 = 2^1*3^2, lcm(2,1) = 2, lcm(3,2) = 6 and 2*6 = 12.
a(300) = 30 because 300 = 2^2*3^1*5^2, lcm(2,2) = 2, lcm(3,1) = 3, lcm(5,2) = 10 and 2*3*10 = 60.

Mathematica

A381588[n_] := Times @@ LCM @@@ FactorInteger[n];
Array[A381588, 100]

Prog

(PARI) a(n) = my(f=factor(n)); prod(i=1, #f~, lcm(f[i, 1], f[i, 2])); \\ Michel Marcus, Mar 02 2025

Crossrefs

Cf. A008473, A008477, A035306, A144338 (fixed points), A369008 (analogous for gcd).

Sequence in context: A308056 A336965 A381203 * A381201 A293303 A333569

Adjacent sequences: A381585 A381586 A381587 * A381589 A381590 A381592

Keyword

nonn,mult,easy,new

Author

Paolo Xausa, Feb 28 2025

Status

approved