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# phi(phi(floor(exp(3!))))=96

This note's credits goes to a comment by Deepak Gowda in this post.

Generate 0 to 100 with only one digit once: the digit 3. You may use any other functions, like the one in the title.

Please enter as much as you can! :)

Note by Kenny Lau
2 years, 8 months ago

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$$\lfloor \sin(3^{\circ})\rfloor = 0$$

$$\text{sgn}(3) = 1$$ (sign function)

$$\phi(3) = 2$$ (Euler's totient phi function)

$$3$$

$$\sigma(3) = 4$$ (divisor sum)

$$\Sigma(3) = 5$$ (prime sum)

$$3! = 6$$

$$\lfloor \csc(3)\rfloor = 7$$

$$\lceil \csc(3)\rceil = 8$$

$$\lfloor\text{antilog}(\tan(3)) \rfloor = 9$$ ($$\text{antilog}(x) = 10^{x}$$)

$$\Sigma(\Sigma(3)) = 10$$

$$p_{\Sigma(3)} = 11$$ (n-th prime number)

$$\sigma(3!) = 12$$

$$F_{\lceil \csc(3)\rceil} = 13$$ (Fibonacci function $$F_{1} = 0, F_{2} = 1, F_{n+2} = F_{n} + F_{n+1}$$)

$$\sigma(F_{\lceil \csc(3)\rceil}) = 14$$

$$\sigma(\lceil \csc(3)\rceil) = 15$$

$$\phi(s(\sigma(\sigma(\sigma(3))))) = 16$$

$$s(\sigma(\sigma(\sigma(3)))) = 17$$ (aliquot sum $$s(n) = \sigma(n) - n$$)

$$\sigma(s(\sigma(\sigma(\sigma(3))))) = 18$$

$$p_{\lceil \csc(3)\rceil} = 19$$

$$\sigma(p_{\lceil \csc(3)\rceil}) = 20$$

$$\lfloor \tan(\tan(\cos(\sin(3^{\circ})))) \rfloor = 21$$

$$\lceil \tan(\tan(\cos(\sin(3^{\circ})))) \rceil = 22$$

$$p_{\lfloor\text{antilog}(\tan(3)) \rfloor} = 23$$

$$(\Sigma(3))! = 24$$ · 2 years, 8 months ago

Actually we can do any prime numbers if we have first 25 numbers. And also prime numbers minus 1 using Euler's totient function. And also Fibonacci numbers. And also Lucas numbers. And blahuhuhuh · 2 years, 8 months ago

I've commented but you've created...

so credits goes to Kenny Lau and Vinay Sipani · 2 years, 8 months ago

Ty... But the credit must go to you.. · 2 years, 8 months ago

• $$\left\lfloor{cotan(3°)}\right\rfloor=20$$
• $$\left\lceil{cotan(3°)}\right\rceil=19$$
• $$\mu(\mu(3))=1$$
• $$\frac{d}{dx}(3)=0$$
• σ(3)=4 where σ(n) is sum of positive divisors.
· 2 years, 8 months ago

Well, $$\frac d{dx}(3)=0$$. · 2 years, 8 months ago

oops yeah...its 0 mis-typo... · 2 years, 8 months ago