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Search: id:A078359
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| A078359 |
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Number of ways to write n as sum of a positive square and a positive cube. |
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+0
2
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| 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0
(list; graph; listen)
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OFFSET
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1,17
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COMMENT
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a(A066650(n))=0, a(A055394(n))>0, a(A078360(n))=1, a(A054402(n))>1.
Earliest entries with a(n)=3 are n=1737, 2089, 2628, 2817. Earliest entries with a(n)=4 are n=1025, 19225, 27289, 29025, 39329, 48025, 54225. Earliest entries with a(n)=5 are n=92025, 540900, 567225, 747225. There are no a(n)>=6 in the range n=1..700000. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 16 2006
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EXAMPLE
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a(1025)=4, as 1025 = 5^2+10^3 = 30^2+5^3 = 31^2+4^3 = 32^2+1^3.
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MAPLE
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interface(prettyprint=0) : A078359 := proc(n) local resul, isq, icu ; resul := 0 ; icu := 1 ; while icu^3 < n do if issqr(n-icu^3) then resul := resul+1 ; fi ; icu := icu+1 ; od ; RETURN(resul) ; end: for n from 1 to 100000 do printf("%d %d ", n, A078359(n)) ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 16 2006
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CROSSREFS
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Adjacent sequences: A078356 A078357 A078358 this_sequence A078360 A078361 A078362
Sequence in context: A089810 A096562 A096563 this_sequence A107329 A085859 A086016
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 25 2002
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