[seqfan] Re: %C A020882 (?)

Ray Chandler rayjchandler at sbcglobal.net
Mon Apr 12 23:19:38 CEST 2010

> A permutation of A020882, that is A119321, needs more terms.
> In conjunction with A159781 (4 different shapes of primitive 
> Pythagorean triangles) and A006278 (2^n different shapes - or 
> should the Beedassy comment read 2^(n-1)?) one may ask:
> i) are there examples of hypotenuses c which appear in 6 
> different primitive Pythagorean triangles?
> ii) does A159781 have a "faster" algorithm if the prime 
> factorization is examined for
>      prime factors of the 4k+1 class? (A correction 6429 -> 
> 6409 in A159781 has been submitted.)

I submitted extensions for A119321 and A119322 earlier today.

Yes, in A006278, comment should read  2^(n-1).

A159781 should be numbers with exactly three distinct prime factors, all of the form 4k+1.
A given value of hypotenuse c will have zero instances if there is a prime factor not of the form 4k+1.
If all the distinct prime factors are of the form 4k+1, then the number of occurances will be 
2^(number of distinct prime factors - 1).
Thus there will be no such hypotenuse c with number of occurrences exactly 6.  


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