A382123 a(n) = sigma(n)*sigma(2*n)/3 for n >= 1.

1, 7, 16, 35, 36, 112, 64, 155, 169, 252, 144, 560, 196, 448, 576, 651, 324, 1183, 400, 1260, 1024, 1008, 576, 2480, 961, 1372, 1600, 2240, 900, 4032, 1024, 2667, 2304, 2268, 2304, 5915, 1444, 2800, 3136, 5580, 1764, 7168, 1936, 5040, 6084, 4032, 2304, 10416, 3249, 6727, 5184, 6860

Offset: 1

Author

Paul D. Hanna, Apr 06 2025

Keywords

• nonn

Comments

For n >= 1, 2*A329963(n) = A087943(k) for some k; this is a consequence of the prime factorization properties of the numbers listed in A329963 and A087943 (see the comments in both entries). That is, two times any term found in A329963 (numbers k such that sigma(k) is not divisible by 3) equals a term found in A087943 (numbers k such that 3 divides sigma(k)). Therefore sigma(n)*sigma(2*n) is divisible by 3 for n >= 1.

Equals the logarithmic derivative of A382124.

Crossrefs

Cf. A382124, A382125, A087943, A329963, A347108.

Cf. A000203, A062731.

Programs

PARI

{a(n) = sigma(n)*sigma(2*n)/3}
for(n=1,52, print1(a(n),", "))

Formula

a(n) = A000203(n) * A062731(n) / 3.

Sum_{k=1..n} a(k) ~ 2*zeta(3)*n^3/3. - Vaclav Kotesovec, Apr 06 2025