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

%I A088822 #21 Jan 27 2019 09:21:54
%S A088822 0,2,5,7,12,15,22,24,27,32,43,46,59,66,71,73,90,93,112,117,124,135,
%T A088822 158,161,166,179,182,189,218,223,254,256,267,284,291,294,331,350,363,
%U A088822 368,409,416,459,470,475,498,545,548,555,560,577,590,643,646,657,664,683
%N A088822 a(n) is the sum of largest prime factors of numbers from 1 to n.
%H A088822 Michael De Vlieger, <a href="/A088822/b088822.txt">Table of n, a(n) for n = 1..10000</a>
%F A088822 a(n) = Pi^2/12 * n^2/log n + O(n^2/log^2 n). - _Charles R Greathouse IV_, Feb 19 2014
%F A088822 a(n) ~ zeta(2) * A088821(n), where zeta(2) = Pi^2/6. - _Thomas Ordowski_, Nov 29 2018
%t A088822 -1 + Accumulate@ Array[FactorInteger[#][[-1, 1]] &, 57] (* _Michael De Vlieger_, Jul 23 2017 *)
%o A088822 (PARI) gpf(n)=if(n<4, n, n=factor(n)[, 1]; n[#n])
%o A088822 a(n)=sum(k=2, n, gpf(k)) \\ _Charles R Greathouse IV_, Feb 19 2014
%o A088822 (GAP) P:=List(List([2..60],n->Reversed(Factors(n))),i->i[1]);;
%o A088822  a:=Concatenation([0],List([1..Length(P)],i->Sum([1..i],k->P[k]))); # _Muniru A Asiru_, Nov 29 2018
%Y A088822 Cf. A046670, A006530, A088821, A088823, A088824, A088825.
%K A088822 nonn
%O A088822 1,2
%A A088822 _Labos Elemer_, Oct 22 2003