

A004144


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


21



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
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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.  JeanChristophe HervĂ©, Nov 17 2013


REFERENCES

S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 98104.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000
S. R. Finch, LandauRamanujan Constant
D. Shanks, Nonhypotenuse numbers, Fib. Quart., 13:4 (1975), pp. 319321.
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==1vecmin(factor(n)[, 1]%4)>1 \\ Charles R Greathouse IV, Apr 16 2012
(Haskell)
import Data.List (elemIndices)
a004144 n = a004144_list !! (n1)
a004144_list = map (+ 1) $ elemIndices 0 a005089_list
 Reinhard Zumkeller, Jan 07 2013


CROSSREFS

Complement of A009003.
Cf. A072437.
Sequence in context: A013939 A209921 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


STATUS

approved



