

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
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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



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:


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



KEYWORD

nonn,easy


AUTHOR



EXTENSIONS



STATUS

approved



