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A215908 Smallest integer that can be represented as the sum of n squares of positive integers in at least n distinct ways. 2
1, 50, 54, 52, 53, 54, 55, 56, 57, 61, 65, 66, 67, 68, 74, 78, 79, 81, 82, 83, 84, 88, 92, 93, 96, 98, 99, 100, 101, 102, 106, 107, 108, 112, 113, 114, 115, 116, 117, 121, 124, 125, 129, 130, 131, 132, 133, 134, 136, 137, 141, 142, 143, 147, 148, 149, 150, 151 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This sequence differs from A052261 first at n=11: a(11) = 65 < A052261(11) = 67. 65 has 12 distinct representations (as the sum of 11 squares of positive integers) whereas 67 has exactly 11.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

EXAMPLE

a(1) =  1 = 1^2.

a(2) = 50 = 1^2+7^2 = 5^2+5^2.

a(3) = 54 = 2^2+2*5^2 = 2*3^2+6^2 = 1^2+2^2+7^2.

a(11) = 65 = 3*1^2+2*2^2+6*3^2 = 2*1^2+5*2^2+3*3^2+4^2 = 1^2+8*2^2+2*4^2 = 6*1^2+3*3^2+2*4^2 = 5*1^2+3*2^2+3*4^2 = 10*2^2+5^2 = 5*1^2+2*2^2+3*3^2+5^2 = 4*1^2+5*2^2+4^2+5^2 = 8*1^2+2*4^2+5^2 = 7*1^2+2*2^2+2*5^2 = 7*1^2+2^2+2*3^2+6^2 = 8*1^2+2*2^2+7^2.

MAPLE

b:= proc(n, i, t) option remember; `if`(n<t, 0, `if`(n=t, 1,

      `if`(t=0, 0, `if`(i>0, b(n, i-1, t), 0)+

      `if`(i^2>n, 0, b(n-i^2, i, t-1)))))

    end:

a:= proc(n) local k;

      for k while b(k, isqrt(k), n)<n do od; k

    end:

seq(a(n), n=1..100);

MATHEMATICA

b[n_, i_, t_] := b[n, i, t] = If[n < t, 0, If[n == t, 1, If[t == 0, 0, If[i > 0, b[n, i-1, t], 0] + If[i^2 > n, 0, b[n-i^2, i, t-1]]]]]; a[n_] := Module[{k}, For[k = 1, b[k, Sqrt[k] // Floor, n] < n, k++]; k]; Table[a[n], {n, 1, 100}] (* Jean-Fran├žois Alcover, Dec 30 2013, translated from Maple *)

CROSSREFS

Cf. A052261.

Sequence in context: A294297 A320673 A081646 * A052261 A295155 A118146

Adjacent sequences:  A215905 A215906 A215907 * A215909 A215910 A215911

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 26 2012

STATUS

approved

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Last modified September 28 12:34 EDT 2020. Contains 337393 sequences. (Running on oeis4.)