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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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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; refs; listen; history; internal format)
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OFFSET
| 1,17
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COMMENTS
| 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
| 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
| 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
| Sequence in context: A089810 A096562 A096563 * A107329 A085859 A086016
Adjacent sequences: A078356 A078357 A078358 * A078360 A078361 A078362
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KEYWORD
| nonn
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 25 2002
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