A193018 -id:A193018 - cp's OEIS frontend

A191090 a(n)^2 is the largest square required when writing n as a partition of squares.

1, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 2, 2, 1, 1, 4, 2, 3, 1, 2, 2, 2, 1, 2, 5, 2, 3, 2, 2, 2, 2, 4, 2, 3, 2, 6, 2, 2, 2, 2, 4, 2, 3, 2, 3, 2, 2, 4, 7, 5, 2, 4, 2, 3, 2, 2, 4, 3, 3, 2, 5, 2, 3, 8, 4, 4, 3, 4, 2, 3, 2, 6, 4, 5, 5, 3, 4, 2, 3, 4, 9, 4, 3, 4, 6, 5

Offset: 1

T. D. Noe, Jul 18 2011

nonn

If we write n as the sum of nondecreasing squares, then a(n) is the largest value such that n = a(n)^2 + ....

			a(8) = 2 because 8 = 2^2 + 2^2.

T. D. Noe, Table of n, a(n) for n = 1..1000

Cf. A191091, A193018.

Table[Last[Union[First /@ Union /@ (DeleteCases[#, 0] & /@ PowersRepresentations[n, 11, 2])]], {n, 100}]

A191091 Least number of squares required when writing n as a sum of squares with the smallest square as large as possible.

Original entry on oeis.org

1, 2, 3, 1, 2, 3, 4, 2, 1, 2, 3, 3, 2, 3, 4, 1, 3, 2, 3, 2, 4, 3, 4, 3, 1, 4, 3, 4, 2, 5, 4, 2, 3, 2, 5, 1, 4, 3, 6, 2, 2, 4, 3, 3, 2, 5, 4, 3, 1, 2, 5, 2, 2, 3, 6, 3, 3, 2, 3, 4, 2, 3, 4, 1, 2, 3, 3, 3, 3, 3, 4, 2, 4, 2, 3, 4, 3, 3, 4, 2, 1, 4, 3, 4, 2, 3, 4

Offset: 1

T. D. Noe, Jul 21 2011

nonn

The smallest value in the sum is A191090. All sums have at most 6 terms for n <= 1000. Is this the largest possible value? For n up to 1000, only 39, 55, 143, 543, and 564 need 6 terms.

			The sum for 30 gives the first sum having 5 terms: 4 + 4 + 4 + 9 + 9.

T. D. Noe, Table of n, a(n) for n = 1..1000

Cf. A191090, A193018.

Table[s=DeleteCases[#, 0]& /@ PowersRepresentations[n,11,2]; t=Last[Union[First /@ Union /@ s]]; Min @@ Length /@ Select[s, #[[1]] == t &], {n, 100}]

cp's OEIS Frontend

A191090 a(n)^2 is the largest square required when writing n as a partition of squares.

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