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Minimum numbers of squares needed to write n! as a sum of nonzero squares.
1

%I #6 Jul 09 2023 02:15:47

%S 1,2,3,3,3,2,3,3,3,4,3,4,3,3,3,3,3,3,3,3,3,3,3,4,4,3,3,3,3,3,3,3,3,3,

%T 3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,3,3,3,3,4,3,3,3,3,3,4,3,3,3,3,3,3,3,3,

%U 3,3,3,3,3,3,3,3,3,4,3,3,3,3,3,3,3,3,3,3,3,3,4,3,3,3,3,4,4,3,3,3,3,3,3,3,3

%N Minimum numbers of squares needed to write n! as a sum of nonzero squares.

%H Dario Alpern, <a href="https://www.alpertron.com.ar/FSQUARES.HTM">Sum of squares web application</a>

%e a(2)=2 because 2!=1^2+1^2; a(3)=3: 3!=6=2^2+1+1; a(6)=2: 6!=720=24^2+12^2

%o See link.

%Y Cf. A000142, A001481, A000419, A004215, A084953.

%K nonn

%O 1,2

%A _Hugo Pfoertner_, Jun 15 2003