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%I #28 Aug 31 2020 11:54:07
%S 2,13,29,37,53,101,173,197,293,421,541,677,709,1021,1069,1117,1373,
%T 1381,1429,1597,1621,1669,1709,1741,1789,1861,1901,1933,2053,2213,
%U 2269,2293,2341,2381,2557,2677,2749,2797,3061,3109,3221,3613,3637,3701
%N Prime numbers of the form x^2+y^2 such that Mobius(x) * Mobius(y) = 1.
%D M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 844.
%H Jean-François Alcover, <a href="/A174049/b174049.txt">Table of n, a(n) for n = 1..1000</a>
%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%H Marc Deléglise and Joël Rivat, <a href="http://projecteuclid.org/euclid.em/1047565447">Computing the summation of the Mobius function</a>, Experiment. Math. 5:4 (1996), pp. 291-295.
%H Primefan, <a href="http://primefan.tripod.com/Mertens2500.html">Mobius and Mertens Values For n=1 to 2500</a>
%H Gérard Villemin, <a href="http://villemin.gerard.free.fr/TABLES/aaaFArit/MobiusMe.htm">Tables des Nombres de Moebius et de Mertens</a>
%e 2 is in the sequence because 2 = 1^2 + 1^2 and mobius(1)*mobius(1) = 1*1 = 1;
%e 13 is a term because 13 = 2^2 + 3^2 and mobius(2)*mobius(3) = (-1)*(-1) = 1.
%p with(numtheory): T:=array(0..50000000): k:=1:for x from 1 to 1000 do: for y from x to 1000 do if mobius(x)* mobius(y)= 1 and isprime(x^2+y^2) then T[k]:=x^2+y^2:k:=k+1 fi od od: mini:=T[1]:ii:=1: for p from 1 to k-1 do for n from 1 to k-1 do if T[n] < mini then mini:= T[n]:ii:=n fi od: print(mini): T[ii]:= 99999999: ii:=1:mini:=T[1] :od:
%t terms = 1000;
%t Reap[Do[p = x^2 + y^2; If[PrimeQ[p] && MoebiusMu[x] MoebiusMu[y] == 1, Sow[p]], {x, terms}, {y, x}]][[2, 1]] // Sort // Take[#, terms]& (* _Jean-François Alcover_, Aug 31 2020 *)
%Y Cf. A008683.
%K nonn
%O 1,1
%A _Michel Lagneau_, Mar 06 2010
%E Corrected and edited by _Michel Lagneau_, Apr 25 2010
%E Typo in name and missing value inserted by _D. S. McNeil_, Nov 20 2010
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