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A255131 n minus the least number of squares that add up to n: a(n) = n - A002828(n). 22
0, 0, 0, 0, 3, 3, 3, 3, 6, 8, 8, 8, 9, 11, 11, 11, 15, 15, 16, 16, 18, 18, 19, 19, 21, 24, 24, 24, 24, 27, 27, 27, 30, 30, 32, 32, 35, 35, 35, 35, 38, 39, 39, 40, 41, 43, 43, 43, 45, 48, 48, 48, 50, 51, 51, 51, 53, 54, 56, 56, 56, 59, 59, 59, 63, 63, 63, 64, 66, 66, 67, 67, 70, 71, 72, 72, 73, 74, 75, 75, 78, 80, 80, 80, 81 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

The associated beanstalk-sequence starts from a(0) as: 0, 3, 6, 8, 11, 15, 16, 18, 21, ... (A276573).

LINKS

Robert Israel, Table of n, a(n) for n = 0..10000

Discussion on the SeqFan mailing list

FORMULA

a(n) = n - A002828(n).

a(n) = A260740(n) + A062535(n).

EXAMPLE

a(0) = 0, because no squares are needed for an empty sum, and 0 - 0 = 0.

a(3) = 0, because 3 cannot be represented as a sum of less than three squares (1+1+1), and 3 - 3 = 0.

a(4) = 3, because 4 can be represented as a sum of just one square (namely 4 itself), and 4 - 1 = 3.

MAPLE

f:= proc(n) local F, x;

   if issqr(n) then return n-1 fi;

   if nops(select(t -> t[1] mod 4 = 3 and t[2]::odd, ifactors(n)[2])) = 0 then return n-2 fi;

   x:= n/4^floor(padic:-ordp(n, 2)/2);

   if x mod 8 = 7 then n-4 else n-3 fi

end proc:

f(0):= 0:

map(f, [$0..100]); # Robert Israel, Mar 27 2018

MATHEMATICA

{0}~Join~Table[n - (If[First@ # > 0, 1, Length[First@ Split@ #] + 1] &@ SquaresR[Range@ 4, n]), {n, 84}] (* Michael De Vlieger, Sep 08 2016, after Harvey P. Dale at A002828 *)

CROSSREFS

Subsequence: A005563.

Cf. A000290, A002828, A062535, A260731, A260732, A260733, A260734, A262689, A276573.

Cf. also A011371, A236840, A260740.

Sequence in context: A142716 A211515 A260740 * A280453 A289903 A285047

Adjacent sequences:  A255128 A255129 A255130 * A255132 A255133 A255134

KEYWORD

nonn

AUTHOR

Antti Karttunen, Feb 24 2015

STATUS

approved

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Last modified October 21 08:47 EDT 2019. Contains 328292 sequences. (Running on oeis4.)