|
%I #10 Feb 25 2023 21:34:14
%S 1,-1,2,0,5,2,9,7,10,5,16,13,26,19,24,22,39,36,55,50,57,46,69,66,71,
%T 58,61,54,83,78,109,107,118,101,108,105,142,123,136,131,172,165,208,
%U 197,202,179,226,223,230,225,242,229,282,279,290,283,302,273,332,327,388,357,364,362
%N Alternating partial sum of A006530.
%C a(2) = -1 is the only negative term of the sequence.
%F a(n) ~ (Pi^2*n^2*log(n/4))/(24*log(n/2)*log(n)) as n -> infinity.
%e a(4) = 0 since the greatest prime factors of {1,2,3,4} are {1,2,3,2} and the alternating sum 1-2+3-2 = 0.
%t a[k_] := Sum[(-1)^(n + 1)*ResourceFunction["LargestPrimeFactor"][n], {n, 1, k}].
%o (PARI) a(n)=if(n>1, vecmax(factor(n)[, 1]), 1); s(k)=sum(n=1, k, a(n)*(-1)^(n+1))
%Y Cf. A006530, A046670.
%K sign
%O 1,3
%A _Luca Onnis_, Feb 11 2023
|
