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TheDag  Per Aspera ad Astra  2yr ago (text post)   2187 thread views

Friday Fun Thread for November 11, 2022

Be advised; this thread is not for serious in depth discussion of weighty topics (we have a link for that), this thread is not for anything Culture War related. This thread is for Fun. You got jokes? Share 'em. You got silly questions? Ask 'em.

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R is for red

O is for orange

Y is for yellow

And G is for green

B is for blue

I for indigo

And V is for violet

And that spells Roy G. Biv

Roy G. Biv is a colourful man.

You'll never see Roy G. Biv.

(Move from reddit wasn't all bad; HTML is fun.)

On an unrelated I am working on a problem related to this. Let be G(N,x) be the fraction of integers up to N, for which the sum-of-divisors function is smaller than x*N, x a real number greater than 0.1 Numerical experiments have convinced me that the limit as N goes to infinity exists, which I will denote simply as G(x). It follows Grönwall's theorem that for finite x, G(x) never equalls one. G(x) can be thought of as a CDF with support the positive reals. For 0<x<1 G(x) appears, again from brute force calculation N=10^7, to be a linear function .627*x (the coefficient is approximate). This graph depicts G(10^7,x) in blue and .627*x in red, showing that for 0<x<1, they appear to overlap.

1: More formally, using the notation from the link:

G(x)=lim_{N->inf} (1/N)*#{1<=n<=N|σ1(n)<=x*N}

Edit: TIL that in the post preview "border" and "font-size" attributes are displayed, but actual posted version stripts them out.

HTML is fun.

I agree, but you used primarily CSS, not HTML.

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