იბრძოლეთ ყველამ ჩემთან ერთად! წინ! თუ არადა უკან მაინც მომყევით, რათა დააფიქსიროთ თუ როგორ იქმნება ახალი მათემატიკა!
Let Q(x) denote the number of square-free integers between 1 and x;
poi(n) denote the product of the indicators of the prime divisors of the positive integer n;
soi(n) denote the sum of the indicators of the prime divisors of the positive integer n;
τ(n) is number of the divisors of the n;
φ(n) is Euler's function;
π(n) is number of the prime numbers between 1 and n;
σ(n) is the sum of the divisors of the positive integer n;
[ ] is integer part;
then
Q(n+1)=Q(n)+[1/poi(n+1)];
Q(n+1)=Q(n)+[rad(n+1)/(n+1)];
Q(n+1)=Q(n)+[log(n+1, rad(n+1))];
Q(n+1)=Q(n)+[soi(rad(n+1))/soi(n+1)];
Q(n+1)=Q(n)+[log(soi(n+1), soi(rad((n+1)))];
π(n+1)=π(n)+[2/τ(n+1)];
π(n+1)=π(n)+[φ(n+1)/n];
π(n+1)=π(n)+[1/soi(n+1)];
π(n+1)=π(n)+[(1+rad(n+1))/σ(n+1)];
π(n+1)=π(n)+[1/(σ(n+1)-rad(n+1))];
π(n+1)=π(n)+[log(σ(n+1), 1+rad(n+1))];
π(n+1)=π(n)+[log(n, φ(n+1))];
π(n+1)=π(n)+[log(τ(n+1), 2)].
Emzari Papava
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