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revised Efficient way to compute $\sum_{i=1}^n \varphi(i) $
expand via A064018
Jul
17
comment primes whose difference is a multiple of $n$
See also oeis.org/A204894
Jul
17
comment Understanding Wright's proof of Landau's theorem
@EricNaslund: OK, I've edited to include it.
Jul
17
revised Understanding Wright's proof of Landau's theorem
expand as requested
Jul
16
comment Understanding Wright's proof of Landau's theorem
@EricNaslund: Yes, only $\Omega_0(x),$ because that's all that's used in the question. I can copy the full definition for you if you're interested.
Jul
16
comment Understanding Wright's proof of Landau's theorem
@Timbuc: the proof seems to assume that theta(x) - x goes to 0, but it doesn't. What don't I get?
Jul
16
asked Understanding Wright's proof of Landau's theorem
Jul
16
answered Do the sum of all prime reciprocals with the digit $3$ converge or diverge?
Jul
14
revised A few questions about Andy Loo's proof of existence of primes between 3n and 4n…
deleted 267 characters in body
Jul
14
comment A few questions about Andy Loo's proof of existence of primes between 3n and 4n…
@virnoy: It looks like the author defines the notation on p. 4. I won't copy it here.
Jul
14
answered A few questions about Andy Loo's proof of existence of primes between 3n and 4n…
Jul
13
revised Sum of primes at minimal $\gt t!$
a_1000
Jul
13
comment Sum of primes at minimal $\gt t!$
@AAron: Of course almost all functions cannot be expressed as formulas, so it should come as no surprise that I gave a function without a formula.
Jul
13
comment Sum of primes at minimal $\gt t!$
@AAron: You seem to be confusing "function" and "formula".
Jul
13
comment Sum of primes at minimal $\gt t!$
The first function is $f(1)=2,f(2)=3,f(3)=5,f(4)=17,$ etc. The rules for $f(n)$ are identical to $a_n$. The second function is $f(1)=4,f(2)=2,f(3)=3,f(4)=5,f(5)=17,$ etc.; it's the same as the first with a 4 prepended. If you mean something other than what you asked, please clarify what you intended.
Jul
13
comment Sum of primes at minimal $\gt t!$
@AAron: Your assertion is incorrect: $t\mapsto a_t$ is precisely such a function. Perhaps you mean something other than "function"? Of course if you want a function which also produces composites, that's easy enough: make $f(1)=4$ and $f(n+1)=a_n$ for all $n>0$.
Jul
13
comment Weierstrass factorization theorem and primality function
@MichaelGaluza: I attempted to address this in another edit. But really, this is a new question!
Jul
13
revised Weierstrass factorization theorem and primality function
forgot -
Jul
13
comment Weierstrass factorization theorem and primality function
@MichaelGaluza: The Weierstrass factorization theorem doesn't let you specify values at the non-zeros, so if you're going to continue it you'll need other tools.
Jul
13
comment Weierstrass factorization theorem and primality function
@MichaelGaluza: I edited the answer. Since your function is not entire, the Weierstrass factorization theorem has nothing to say about it.