A390692 a(n) is the smallest positive integer such that a(n) * n is a Loeschian number (A003136).

1, 2, 1, 1, 5, 2, 1, 2, 1, 10, 11, 1, 1, 2, 5, 1, 17, 2, 1, 5, 1, 22, 23, 2, 1, 2, 1, 1, 29, 10, 1, 2, 11, 34, 5, 1, 1, 2, 1, 10, 41, 2, 1, 11, 5, 46, 47, 1, 1, 2, 17, 1, 53, 2, 55, 2, 1, 58, 59, 5, 1, 2, 1, 1, 5, 22, 1, 17, 23, 10, 71, 2, 1, 2, 1, 1, 11, 2, 1, 5, 1, 82, 83, 1, 85, 2, 29, 22, 89, 10, 1, 23, 1, 94, 5, 2, 1, 2, 11, 1

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

Multiplicative with a(p^e) = p^(e mod 2) if p == 2 (mod 3), and a(p^e) = 1 otherwise.

a(n) = n / A390691(n).

a(n) = n if and only if n is squarefree and all the prime factors of n are == 2 (mod 3).

a(n) = 1 if and only if n is in A003136.

Mathematica

f[p_, e_] := If[Mod[p, 3] == 2, p^Mod[e, 2], 1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

Prog

(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i, 1]%3 == 2, f[i, 1]^(f[i, 2] % 2), 1)); }

Crossrefs

Cf. A003136, A363340, A390691.

Sequence in context: A047888 A330964 A397044 * A128704 A075259 A307877

Adjacent sequences: A390689 A390690 A390691 * A390693 A390694 A390695

Keyword

nonn,mult,easy

Author

Amiram Eldar, Nov 15 2025

Status

approved