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 A004144 Nonhypotenuse numbers (indices of positive squares that are not the sums of 2 distinct nonzero squares). (Formerly M0542) 43
 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, 42, 43, 44, 46, 47, 48, 49, 54, 56, 57, 59, 62, 63, 64, 66, 67, 69, 71, 72, 76, 77, 79, 81, 83, 84, 86, 88, 92, 93, 94, 96, 98, 99, 103, 107, 108, 112, 114, 118, 121, 124, 126, 127 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also numbers with no prime factors of form 4*k+1. m is a term iff A072438(m) = m. Density 0. - Charles R Greathouse IV, Apr 16 2012 Closed under multiplication. Primitive elements are A045326, 2 and the primes of form 4*k+3. - Jean-Christophe Hervé, Nov 17 2013 REFERENCES Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 98-104. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Evan M. Bailey, Table of n, a(n) for n = 1..20000 (Terms 1..1000 from T. D. Noe) Evan M. Bailey, a004114.cpp. Steven R. Finch, Landau-Ramanujan Constant [Broken link] Steven R. Finch, Landau-Ramanujan Constant [From the Wayback machine] Daniel Shanks, Non-hypotenuse numbers, Fib. Quart., Vol. 13, No. 4 (1975), pp. 319-321. Eric Weisstein's World of Mathematics, Pythagorean Triple. FORMULA A005089(a(n)) = 0. - Reinhard Zumkeller, Jan 07 2013 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 MATHEMATICA fQ[n_] := If[n > 1, First@ Union@ Mod[ First@# & /@ FactorInteger@ n, 4] != 1, True]; Select[ Range@ 127, fQ] A004144 = Select[Range, Length@Reduce[s^2 + t^2 == s # && s > t > 0, Integers] == 0 &] (* Gerry Martens, Jun 09 2020 *) PROG (PARI) is(n)=n==1||vecmin(factor(n)[, 1]%4)>1 \\ Charles R Greathouse IV, Apr 16 2012 (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 (Haskell) import Data.List (elemIndices) a004144 n = a004144_list !! (n-1) a004144_list = map (+ 1) \$ elemIndices 0 a005089_list -- Reinhard Zumkeller, Jan 07 2013 CROSSREFS Complement of A009003. Cf. A000290, A002145, A005089, A072437, A244659, A244662. The subsequence of primes is A045326. Sequence in context: A209921 A268377 A201010 * A124391 A200381 A050118 Adjacent sequences:  A004141 A004142 A004143 * A004145 A004146 A004147 KEYWORD nonn AUTHOR EXTENSIONS More terms from Reinhard Zumkeller, Jun 17 2002 Name clarified by Evan M. Bailey, Sep 17 2019 STATUS approved

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Last modified July 2 06:01 EDT 2022. Contains 354985 sequences. (Running on oeis4.)