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A022544
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Numbers that are not the sum of 2 squares.
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30
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3, 6, 7, 11, 12, 14, 15, 19, 21, 22, 23, 24, 27, 28, 30, 31, 33, 35, 38, 39, 42, 43, 44, 46, 47, 48, 51, 54, 55, 56, 57, 59, 60, 62, 63, 66, 67, 69, 70, 71, 75, 76, 77, 78, 79, 83, 84, 86, 87, 88, 91, 92, 93, 94, 95, 96, 99, 102, 103, 105, 107, 108, 110, 111, 112, 114, 115, 118, 119, 120, 123, 124, 126, 127, 129, 131, 132, 133, 134, 135, 138, 139, 140, 141, 142, 143, 147, 150, 151, 152, 154, 155, 156, 158, 159, 161, 163, 165, 166, 167, 168, 171, 172, 174, 175, 176, 177, 179, 182, 183, 184, 186, 187, 188, 189, 190, 191, 192, 195, 198, 199
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Conjecture: if n is not the sum of 2 squares sigma(n)==0 mod 4 (the converse does not hold). - Benoit Cloitre (benoit7848c(AT)orange.fr), May 19 2002
lim n->inf a(n)/n = 1.
Complement of A000415 in the nonsquare positive integers A000037. [From Max Alekseyev (maxale(AT)gmail.com), Jan 21 2010]
Integers with an equal number of 4k+1 and 4k+3 divisors [From Ant King (mathstutoring(AT)ntlworld.com), Oct 05 2010]
A000161(a(n)) = 0; A070176(a(n)) > 0; A046712 is a subsequence. [Reinhard Zumkeller, Feb 04 2012, Aug 16 2011]
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REFERENCES
| S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 98-104.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..10000
S. R. Finch, Landau-Ramanujan Constant
Index entries for sequences related to sums of squares
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FORMULA
| Numbers having some prime factor p == 3 (mod 4) to an odd power. sigma(n) == 0 (mod 4) because of this prime factor. Every n == 3 (mod 4) is an element. First differences are always 1, 2, 3 or 4, each occurring infinitely often. - David W. Wilson (davidwwilson(AT)comcast.net), Mar 09 2005
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MATHEMATICA
| Select[Range[199], Length[PowersRepresentations[ #, 2, 2]] == 0 &] [From Ant King (mathstutoring(AT)ntlworld.com), Oct 05 2010]
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PROG
| (PARI) for(n=0, 200, if(sum(i=0, n, sum(j=0, i, if(i^2+j^2-n, 0, 1)))==0, print1((n), ", ")))
(Haskell)
import Data.List (elemIndices)
a022544 n = a022544_list !! (n-1)
a022544_list = elemIndices 0 a000161_list
-- Reinhard Zumkeller, Aug 16 2011
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CROSSREFS
| Complement of A001481.
Cf. A018825, A025284, A000404, A007692.
Sequence in context: A136272 A101184 A087643 * A194366 A091067 A120511
Adjacent sequences: A022541 A022542 A022543 * A022545 A022546 A022547
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KEYWORD
| nonn,nice,changed
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), May 19 2002
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