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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

A005089(a(n)) = 0. - Reinhard Zumkeller, Jan 07 2013

Closed under multiplication. Primitive elements are 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]

D. Shanks, Non-hypotenuse numbers, Fib. Quart., 13:4 (1975), pp. 319-321.

Eric Weisstein's World of Mathematics, Pythagorean Triple

Index entries for sequences related to sums of squares

MATHEMATICA

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

PROG

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

(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, A072437.

Sequence in context: A209921 A268377 A201010 * A124391 A200381 A050118

Adjacent sequences:  A004141 A004142 A004143 * A004145 A004146 A004147

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

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 January 25 16:42 EST 2020. Contains 331245 sequences. (Running on oeis4.)