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 A275740 Sums of the next n consecutive nonsquare integers. 1
 0, 2, 8, 21, 46, 83, 136, 210, 306, 426, 575, 758, 972, 1223, 1519, 1855, 2236, 2669, 3156, 3694, 4290, 4956, 5678, 6467, 7332, 8269, 9278, 10368, 11548, 12804, 14148, 15593, 17126, 18753, 20485, 22325, 24262, 26308, 28481, 30756, 33148 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Row sums of nonsquare integers (A000037), seen as a regular triangle: . 2 | 2, 8 | 3, 5, 21 | 6, 7, 8, 46 | 10, 11, 12, 13, 83 | 14, 15, 17, 18, 19, 136 | 20, 21, 22, 23, 24, 26, 210 | 27, 28, 29, 30, 31, 32, 33, 306 | 34, 35, 37, 38, 39, 40, 41, 42, ... The equivalent for all integers are A006003 (starting from 1), A229183 (starting from 2) and A027480 (starting from 0). There are several sequences close to nonsquares whose sum of groups of n terms starts like this sequence, notably A028761, A158276, A167759. LINKS Robert Israel, Table of n, a(n) for n = 0..10000 MAPLE R:= 0: s:= 1: for n from 1 to 100 do if floor(sqrt(s+n)) = floor(sqrt(s)) then R:= R, n*s + n*(n+1)/2; s:= s+n; else R:= R, n*s + n*(n+1)/2 - floor(sqrt(s+n))^2 + s+n+1; s:= s+n+1; fi od: R; # Robert Israel, Oct 02 2022 MATHEMATICA Table[Sum[ i + Floor[1/2 + Sqrt[i]], {i, n (n - 1)/2 + 1, (n + 1) (n)/2}], {n, 0, 40}] Join[{0}, Module[{nn=1000, nsi, len}, nsi=Select[Range[nn], !IntegerQ[Sqrt[#]]&]; len=Floor[ (Sqrt[ 8*Length[nsi]+1]-1)/2]; Total/@TakeList[nsi, Range[len]]]] (* Harvey P. Dale, Jan 04 2024 *) CROSSREFS Cf. A000037, A006003, A229183, A027480. Sequence in context: A212981 A051744 A062443 * A141582 A192692 A182704 Adjacent sequences: A275737 A275738 A275739 * A275741 A275742 A275743 KEYWORD nonn,easy AUTHOR Olivier Gérard, Aug 07 2016 EXTENSIONS Definition clarified by Harvey P. Dale, Jan 04 2024 STATUS approved

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Last modified May 20 11:25 EDT 2024. Contains 372712 sequences. (Running on oeis4.)