A072107 a(n) = Sum_{k=1..n} A014963(k).

1, 3, 6, 8, 13, 14, 21, 23, 26, 27, 38, 39, 52, 53, 54, 56, 73, 74, 93, 94, 95, 96, 119, 120, 125, 126, 129, 130, 159, 160, 191, 193, 194, 195, 196, 197, 234, 235, 236, 237, 278, 279, 322, 323, 324, 325, 372, 373, 380, 381, 382, 383, 436, 437, 438, 439, 440, 441

Offset: 1

Author

Benoit Cloitre, Jun 19 2002

Keywords

• easy
• nonn

Comments

Is there an expression for lim_{n -> infinity} a(n)/n^2?

Equals row sums of triangle A140582. - Gary W. Adamson, May 17 2008

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Vaclav Kotesovec, Plot of a(n) / (n^2/log(n)) for n = 1..10^9

Crossrefs

Cf. A140582, A014963.

Programs

Mathematica

Accumulate[Table[Exp[MangoldtLambda[n]], {n, 1, 60}]] (* Amiram Eldar, May 05 2022 *)

PARI

for(n=2,100,print1(1+sum(k=2,n,if(if(omega(k)-1,0,1)*component(component(factor(k),1),1),if(omega(k)-1,0,1)*component(component(factor(k),1),1),1)),","))

Formula

Conjecture: a(n) ~ n^2/(2*log(n)). - Vaclav Kotesovec, Jan 30 2025