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%I M0542 #78 Jan 29 2022 04:22:23
%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 (indices of positive 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 Closed under multiplication. Primitive elements are A045326, 2 and the primes of form 4*k+3. - _Jean-Christophe Hervé_, Nov 17 2013
%D Steven 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 Evan M. Bailey, <a href="/A004144/b004144.txt">Table of n, a(n) for n = 1..20000</a> (Terms 1..1000 from T. D. Noe)
%H Evan M. Bailey, <a href="/A004144/a004144.cpp.txt">a004114.cpp</a>.
%H Steven R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/constant/lr/lr.html">Landau-Ramanujan Constant</a> [Broken link]
%H Steven R. Finch, <a href="http://web.archive.org/web/20010605004309/http://www.mathsoft.com/asolve/constant/lr/lr.html">Landau-Ramanujan Constant</a> [From the Wayback machine]
%H Daniel Shanks, <a href="http://www.fq.math.ca/Scanned/13-4/shanks.pdf">Non-hypotenuse numbers</a>, Fib. Quart., Vol. 13, No. 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>.
%F A005089(a(n)) = 0. - _Reinhard Zumkeller_, Jan 07 2013
%F The number of terms below x is ~ (A * x / sqrt(log(x))) * (1 + C/log(x) + O(1/log(x)^2)), where A = A244659 and C = A244662 (Shanks, 1975). - _Amiram Eldar_, Jan 29 2022
%t fQ[n_] := If[n > 1, First@ Union@ Mod[ First@# & /@ FactorInteger@ n, 4] != 1, True]; Select[ Range@ 127, fQ]
%t A004144 = Select[Range[127],Length@Reduce[s^2 + t^2 == s # && s > t > 0, Integers] == 0 &] (* _Gerry Martens_, Jun 09 2020 *)
%o (PARI) is(n)=n==1||vecmin(factor(n)[,1]%4)>1 \\ _Charles R Greathouse IV_, Apr 16 2012
%o (PARI) list(lim)=my(v=List(),u=vectorsmall(lim\=1)); forprimestep(p=5,lim,4, forstep(n=p,lim,p, u[n]=1)); for(i=1,lim, if(u[i]==0, listput(v,i))); u=0; Vec(v) \\ _Charles R Greathouse IV_, Jan 13 2022
%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. A000290, A002145, A005089, A072437, A244659, A244662.
%Y The subsequence of primes is A045326.
%K nonn
%O 1,2
%A _N. J. A. Sloane_
%E More terms from _Reinhard Zumkeller_, Jun 17 2002
%E Name clarified by _Evan M. Bailey_, Sep 17 2019
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