A390691 The largest divisor of n that is a Loeschian number (A003136).

1, 1, 3, 4, 1, 3, 7, 4, 9, 1, 1, 12, 13, 7, 3, 16, 1, 9, 19, 4, 21, 1, 1, 12, 25, 13, 27, 28, 1, 3, 31, 16, 3, 1, 7, 36, 37, 19, 39, 4, 1, 21, 43, 4, 9, 1, 1, 48, 49, 25, 3, 52, 1, 27, 1, 28, 57, 1, 1, 12, 61, 31, 63, 64, 13, 3, 67, 4, 3, 7, 1, 36, 73, 37, 75, 76

Offset

1,3

Comments

The number of these divisors is A375325(n) and their sum is A390690(n).

Links

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

Formula

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

a(n) = n / A390692(n).

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

a(n) = 1 if and only if n is squarefree and all the prime factors of n are == 2 (mod 3).

Mathematica

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

Prog

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

Crossrefs

Cf. A003136, A371015, A375325, A390690, A390692.

Sequence in context: A205547 A169782 A131228 * A238558 A131129 A390038

Adjacent sequences: A390688 A390689 A390690 * A390692 A390693 A390694

Keyword

nonn,mult,easy

Author

Amiram Eldar, Nov 15 2025

Status

approved