A088822 a(n) is the sum of largest prime factors of numbers from 1 to n.

0, 2, 5, 7, 12, 15, 22, 24, 27, 32, 43, 46, 59, 66, 71, 73, 90, 93, 112, 117, 124, 135, 158, 161, 166, 179, 182, 189, 218, 223, 254, 256, 267, 284, 291, 294, 331, 350, 363, 368, 409, 416, 459, 470, 475, 498, 545, 548, 555, 560, 577, 590, 643, 646, 657, 664, 683

Offset: 1

Author

Labos Elemer, Oct 22 2003

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A046670, A006530, A088821, A088823, A088824, A088825.

Programs

GAP

P:=List(List([2..60],n->Reversed(Factors(n))),i->i[1]);;
 a:=Concatenation([0],List([1..Length(P)],i->Sum([1..i],k->P[k]))); # Muniru A Asiru, Nov 29 2018

Mathematica

-1 + Accumulate@ Array[FactorInteger[#][[-1, 1]] &, 57] (* Michael De Vlieger, Jul 23 2017 *)

PARI

gpf(n)=if(n<4, n, n=factor(n)[, 1]; n[#n])
a(n)=sum(k=2, n, gpf(k)) \\ Charles R Greathouse IV, Feb 19 2014

Formula

a(n) = Pi^2/12 * n^2/log n + O(n^2/log^2 n). - Charles R Greathouse IV, Feb 19 2014

a(n) ~ zeta(2) * A088821(n), where zeta(2) = Pi^2/6. - Thomas Ordowski, Nov 29 2018