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Search: id:A124978
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| A124978 |
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Smallest number which has exactly n different partitions as a sum of 4 squares x^2+y^2+z^2+t^2. |
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+0
2
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| 1, 4, 18, 34, 50, 66, 82, 114, 90, 130, 150, 178, 162, 198, 318, 210, 250, 234, 322, 406, 465, 330, 306, 402, 462, 390, 474, 378, 490, 486, 654, 610, 522, 450, 778, 678, 642, 570, 666, 726, 594, 714, 770, 774, 986, 630, 738, 945, 1035, 850, 1222, 978, 1014, 918
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Is it known that a(n) always exists? - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Dec 18 2006
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
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EXAMPLE
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a(4)=34 because 34 is smallest number which has 4 partitions 34=4^2+3^2+3^2+0^2 = 4^2+4^2+1^2+1^2 = 5^2+2^2+2^2+1^2 = 5^2+3^2+0^2+0^2
a(3)=18 which has 3 partitions 18=0^2+0^2+3^2+3^2=0^2+1^2+1^2+4^2=1^2+2^2+2^2+3^2.
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PROGRAM
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(PARI) cnt4sqr(n)={ local(cnt=0, t2) ; for(x=0, floor(sqrt(n)), for(y=x, floor(sqrt(n-x^2)), for(z=y, floor(n-x^2-y^2), t2=n-x^2-y^2-z^2 ; if( t2>=z^2 && issquare(n-x^2-y^2-z^2), cnt++ ; ) ; ) ; ) ; ) ; return(cnt) ; } A124978(n)= { local(a=1) ; while(1, if( cnt4sqr(a)==n, return(a) ; ) ; a++ ; ) ; } { for(n=1, 100, print(n, " ", A124978(n)) ; ) ; } - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 29 2006
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CROSSREFS
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Cf. A006431, A094942, A124979-A124983, A000378, A002635, A061262
Sequence in context: A092116 A083969 A110621 this_sequence A031081 A009956 A031303
Adjacent sequences: A124975 A124976 A124977 this_sequence A124979 A124980 A124981
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KEYWORD
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nonn
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AUTHOR
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Artur Jasinski (grafix(AT)csl.pl), Nov 14 2006
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EXTENSIONS
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Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 29 2006
More terms from Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Dec 18 2006
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