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Search: id:A004431
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| A004431 |
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Numbers that are the sum of 2 distinct nonzero squares. |
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26
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| 5, 10, 13, 17, 20, 25, 26, 29, 34, 37, 40, 41, 45, 50, 52, 53, 58, 61, 65, 68, 73, 74, 80, 82, 85, 89, 90, 97, 100, 101, 104, 106, 109, 113, 116, 117, 122, 125, 130, 136, 137, 145, 146, 148, 149, 153, 157, 160, 164, 169, 170, 173, 178, 180, 181, 185, 193, 194, 197
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Increasing different terms of A055096 (5, 10, 13, 17) . First nine terms are identical. [From Paul Curtz (bpcrtz(AT)free.fr), Sep 08 2008]
53=2^2+7^2, and, of course, (53*2)^2+(53*7)^2=53^3 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 25 2009]
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
Index entries for sequences related to sums of squares
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FORMULA
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Numbers whose prime factorization includes at least one prime congruent to 1 mod 4 and any prime factor conguent to 3 mod 4 has even multiplicity. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), May 03 2006
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EXAMPLE
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53 = 7^2+2^2, so 53 is in the sequence.
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MATHEMATICA
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lst={}; q=-1; Do[Do[x=a^2; Do[y=b^2; If[x+y==n, If[n!=q, AppendTo[lst, n]; q=n]], {b, Floor[(n-x)^(1/2)], a+1, -1}], {a, Floor[n^(1/2)], 1, -1}], {n, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 22 2009]
lst = {}; Do[ a = 2 m*n; b = m^2 - n^2; c = m^2 + n^2; AppendTo[lst, c], {m, 100}, {n, m - 1}]; Take[ Union@ lst, 63] [From Robert G. Wilson v (rgwv(AT)rgwv.co), May 02 2009]
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PROGRAM
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(PARI) isA004431(n)={ vecmin((n=factor(n)~%4)[1, ])==1 | return; for( i=1, #n, n[1, i]==3 & n[2, i]%2 & return); 1 } [From M. F. Hasler (MHasler(AT)univ-ag.fr), Feb 06 2009]
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CROSSREFS
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Cf. A009000, A009003, A024507, A004431. Complement of A004439.
Cf. A009177, A118882.
Sequence in context: A050127 A072284 A024507 this_sequence A025302 A055096 A132777
Adjacent sequences: A004428 A004429 A004430 this_sequence A004432 A004433 A004434
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KEYWORD
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nonn,new
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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