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Irregular triangle read by rows in which the n-th row gives the prime factors of 4*n^2 + 1 with repetition.
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%I #20 Nov 11 2024 03:48:32

%S 5,17,37,5,13,101,5,29,197,257,5,5,13,401,5,97,577,677,5,157,17,53,5,

%T 5,41,13,89,1297,5,17,17,1601,5,353,13,149,29,73,5,461,41,61,5,541,

%U 2917,3137,5,673,13,277,5,769,17,241,4357,5,5,5,37,13,13,29,5,17,61,5477,53

%N Irregular triangle read by rows in which the n-th row gives the prime factors of 4*n^2 + 1 with repetition.

%C These numbers are all of the form 4m+1.

%e Triangle begins:

%e 5;

%e 17;

%e 37;

%e 5, 13;

%e 101;

%e 5, 29;

%e 197;

%e 257;

%e 5, 5, 13;

%e 401;

%e 5, 97;

%e 577;

%e ...

%t Flatten[Table[Table[First[#],{Last[#]}]&/@FactorInteger[4*n^2+1], {n,60}]] (* _Harvey P. Dale_, Dec 19 2011 *)

%o (PARI) \\ here ifactor(n) gives n-th row of A027746.

%o ifactor(n) = { local(f,j,k,flist); flist=[]; f=Vec(factor(n)); for(j=1,length(f[1]), for(k = 1,f[2][j],flist = concat(flist,f[1][j]) ); ); return(flist) }

%o row(n)= { ifactor(4*n^2+1) }

%Y Cf. A027746 (similar triangle for n).

%K nonn,tabf

%O 1,1

%A _Cino Hilliard_, Aug 26 2006