A071825 a(n) = (number of x with largest prime factor of the form 4k+3 less than or equal to n) minus (number of x with largest prime factor of the form 4k+1 less than or equal to n).
0, 0, 1, 1, 0, 1, 2, 2, 3, 2, 3, 4, 3, 4, 3, 3, 2, 3, 4, 3, 4, 5, 6, 7, 6, 5, 6, 7, 6, 5, 6, 6, 7, 6, 7, 8, 7, 8, 7, 6, 5, 6, 7, 8, 7, 8, 9, 10, 11, 10, 9, 8, 7, 8, 9, 10, 11, 10, 11, 10, 9, 10, 11, 11, 10, 11, 12, 11, 12, 13, 14, 15, 14, 13, 12, 13, 14, 13, 14, 13, 14, 13, 14, 15, 14, 15, 14, 15
Offset: 1
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
- Robert Israel, Log-log plot of (n, a(n)) for 1 <= n <= 10^6
Programs
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Maple
f:= proc(n) local t; t:= max(numtheory:-factorset(n)) mod 4; if t = 3 then 1 elif t= 1 then -1 else 0 fi end proc: ListTools:-PartialSums(map(f, [$1..100])); # Robert Israel, Nov 05 2024
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PARI
for(n=1,200,print1(sum(i=2,n,if((component(component(factor(i),1),omega(i))-3)%4,0,1))-sum(i=2,n,if((component(component(factor(i),1),omega(i))-1)%4,0,1)),","))
Formula
Extensions
Missing a(1)=0 inserted by Sean A. Irvine, Aug 16 2024
Comments