A228423 Sum of the squared primes less than or equal to n.

0, 0, 0, 4, 4, 4, 4, 4, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87

Offset

1,4

Links

Table of n, a(n) for n=1..67.

Formula

a(n) = Sum_{ i <= n | Omega(i) = 2} i * (1 - mu(i)).

a(n) = A081738(A000196(n)). - Michel Marcus, Aug 20 2023

Example

a(10) = 13; 4 and 9 are the only squared primes less than or equal to 10 and their sum is 13.

Maple

with(numtheory); a:=n->add('if'(bigomega(i)=2, i*(1-mobius(i)), 0), i=1..n); seq(a(n), n=1..100);

Mathematica

With[{sp=Prime[Range[10]]^2}, Table[Total[Select[sp, #<=n&]], {n, 100}]] (* Harvey P. Dale, Nov 11 2016 *)

Crossrefs

Cf. A024450.

Cf. A081738, A000196.

Sequence in context: A048760 A287392 A035627 * A165923 A228729 A174444

Adjacent sequences: A228420 A228421 A228422 * A228424 A228425 A228426

Keyword

nonn

Author

Wesley Ivan Hurt, Nov 09 2013

Status

approved