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A164098 Numbers of the form n * (k_1^2 + k_2^2 + ... + k_n^2). 0
1, 4, 9, 10, 16, 18, 20, 25, 26, 27, 28, 33, 34, 36, 40, 42, 48, 49, 50, 51, 52, 54, 55, 57, 58, 60, 63, 64, 65, 66, 68, 70, 72, 74, 76, 78, 80, 81, 82, 84, 85, 87, 88, 90, 91, 92, 95, 99, 100, 102, 104, 105, 106, 108, 110, 112, 114, 115, 116, 120, 121, 122, 123, 124, 125 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

From Franklin T. Adams-Watters, Aug 29 2009: (Start)

The k_i must all be positive integers.

Note that every integer > 33 is the sum of 5 positive squares, and for n > 5, every integer > n+13 is the sum of n positive squares. (End)

LINKS

Table of n, a(n) for n=1..65.

EXAMPLE

34 = 2*(4^2 + 1^2), 42 = 3*(3^2 + 2^2 + 1^2), thus 34 and 42 are in the sequence.

PROG

(PARI) issumsqs(n, k) = if(n<=0||k<=0, return(k==0&&n==0)); forstep(j=sqrtint(n), max(sqrtint(n\k), 1), -1, if(issumsqs(n-j^2, k-1), return(1))); 0

isa(n)=local(ds); ds=divisors(n); for(k=1, (#ds+1)\2, if(issumsqs(n\ds[k], ds[k]), return(1))); 0

for(n=1, 200, if(isa(n), print1(n", "))) \\ Franklin T. Adams-Watters, Aug 29 2009

CROSSREFS

Cf. A000290, A000404, A000408, A000414, A047700, A111178. [From Franklin T. Adams-Watters, Aug 29 2009]

Sequence in context: A191912 A191911 A329476 * A007936 A050943 A010406

Adjacent sequences:  A164095 A164096 A164097 * A164099 A164100 A164101

KEYWORD

nonn

AUTHOR

Jonas Wallgren, Aug 10 2009, Aug 17 2009

EXTENSIONS

More terms from Franklin T. Adams-Watters, Aug 29 2009

STATUS

approved

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Last modified October 18 08:58 EDT 2021. Contains 348067 sequences. (Running on oeis4.)