A348675 a(n) = Sum_{k=0..n-1} Omega(n^2-k^2).

0, 3, 6, 10, 14, 18, 21, 27, 31, 35, 39, 44, 48, 54, 58, 64, 68, 74, 77, 83, 87, 91, 96, 102, 107, 112, 117, 123, 127, 132, 135, 144, 149, 153, 158, 164, 167, 173, 178, 184, 190, 195, 199, 205, 210, 215, 219, 227, 231, 238, 242, 247, 252, 258, 262, 269, 273, 278

Offset

1,2

Links

Table of n, a(n) for n=1..58.

Formula

a(n) = Sum_{k=0..n-1} A001222(A094728(n,k)).

Example

For n = 3, row 3 of A094728 is 9, 8, 5, and a(3) = Omega(9)+Omega(8)+Omega(5) = 2+3+1 = 6.

Maple

a := n -> add(NumberTheory:-NumberOfPrimeFactors(n*n - k*k), k = 0..n-1):
seq(a(n), n = 1..58);

Mathematica

a[n_] := Sum[PrimeOmega[n^2 - k^2], {k, 0, n - 1}]; Array[a, 60] (* Amiram Eldar, Oct 30 2021 *)

Prog

(PARI) a(n) = sum(k=0, n-1, bigomega(n^2-k^2)); \\ Michel Marcus, Oct 30 2021

Crossrefs

Cf. A001222, A094728.

Sequence in context: A310061 A310062 A310063 * A338074 A310064 A113127

Adjacent sequences: A348672 A348673 A348674 * A348676 A348677 A348678

Keyword

nonn

Author

Oscar Granfeldt, Oct 29 2021

Status

approved