A390262 Multiplicative sequence a(n) with a(p^e) = ((p + 1)^2 * p^(e-1) - 2) * p^(e-1) for prime p and e > 0.

1, 7, 14, 32, 34, 98, 62, 136, 138, 238, 142, 448, 194, 434, 476, 560, 322, 966, 398, 1088, 868, 994, 574, 1904, 890, 1358, 1278, 1984, 898, 3332, 1022, 2272, 1988, 2254, 2108, 4416, 1442, 2786, 2716, 4624, 1762, 6076, 1934, 4544, 4692, 4018, 2302, 7840, 3122, 6230, 4508, 6208, 2914, 8946

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..10000

Formula

Dirichlet g.f.: zeta(s-2) * (zeta(s-1))^2 / (zeta(s) * zeta(2*s-2)).

Dirichlet convolution of A007434 and A298473.

Sum_{k=1..n} a(k) ~ 5 * n^3 / (6*zeta(3)). - Amiram Eldar, Oct 30 2025

Mathematica

f[p_, e_] := ((p+1)^2*p^(e-1) - 2)*p^(e-1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 30 2025 *)

Prog

(PARI) a(n) = { my(f = factor(n)); prod(i=1, #f~, ((f[i, 1]+1)^2 * f[i, 1]^(f[i, 2]-1)-2)*f[i, 1]^(f[i, 2]-1)) }

Crossrefs

Cf. A007434, A298473.

Sequence in context: A058530 A293359 A134384 * A352851 A304143 A055780

Adjacent sequences: A390259 A390260 A390261 * A390263 A390264 A390265

Keyword

nonn,easy,mult

Author

Werner Schulte, Oct 30 2025

Status

approved