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A004144 Nonhypotenuse numbers (squares that are not the sums of 2 distinct nonzero squares).
(Formerly M0542)
21

%I M0542

%S 1,2,3,4,6,7,8,9,11,12,14,16,18,19,21,22,23,24,27,28,31,32,33,36,38,

%T 42,43,44,46,47,48,49,54,56,57,59,62,63,64,66,67,69,71,72,76,77,79,81,

%U 83,84,86,88,92,93,94,96,98,99,103,107,108,112,114,118,121,124,126,127

%N Nonhypotenuse numbers (squares that are not the sums of 2 distinct nonzero squares).

%C Also numbers with no prime factors of form 4*k+1.

%C m is a term iff A072438(m) = m.

%C Density 0. - _Charles R Greathouse IV_, Apr 16 2012

%C A005089(a(n)) = 0. - _Reinhard Zumkeller_, Jan 07 2013

%C Closed under multiplication. Primitive elements are 2 and the primes of form 4*k+3. - _Jean-Christophe Hervé_, Nov 17 2013

%D S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 98-104.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A004144/b004144.txt">Table of n, a(n) for n = 1..1000</a>

%H S. R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/constant/lr/lr.html">Landau-Ramanujan Constant</a>

%H D. Shanks, <a href="http://www.fq.math.ca/Scanned/13-4/shanks.pdf">Non-hypotenuse numbers</a>, Fib. Quart., 13:4 (1975), pp. 319-321.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PythagoreanTriple.html">Pythagorean Triple</a>

%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>

%t fQ[n_] := If[n > 1, First@ Union@ Mod[ First@# & /@ FactorInteger@ n, 4] != 1, True]; Select[ Range@ 127, fQ]

%o (PARI) is(n)=n==1||vecmin(factor(n)[,1]%4)>1 \\ _Charles R Greathouse IV_, Apr 16 2012

%o (Haskell)

%o import Data.List (elemIndices)

%o a004144 n = a004144_list !! (n-1)

%o a004144_list = map (+ 1) $ elemIndices 0 a005089_list

%o -- _Reinhard Zumkeller_, Jan 07 2013

%Y Complement of A009003.

%Y Cf. A072437.

%K nonn

%O 1,2

%A _N. J. A. Sloane_.

%E More terms from _Reinhard Zumkeller_, Jun 17 2002

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Last modified July 29 21:54 EDT 2014. Contains 245046 sequences.