OFFSET
1,3
COMMENTS
a(2) = -1 is the only negative term of the sequence.
FORMULA
a(n) ~ (Pi^2*n^2*log(n/4))/(24*log(n/2)*log(n)) as n -> infinity.
EXAMPLE
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.
MATHEMATICA
a[k_] := Sum[(-1)^(n + 1)*ResourceFunction["LargestPrimeFactor"][n], {n, 1, k}].
PROG
(PARI) a(n)=if(n>1, vecmax(factor(n)[, 1]), 1); s(k)=sum(n=1, k, a(n)*(-1)^(n+1))
CROSSREFS
KEYWORD
sign
AUTHOR
Luca Onnis, Feb 11 2023
STATUS
approved