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A000419 Numbers that are the sum of 3 but no fewer nonzero squares. 11
3, 6, 11, 12, 14, 19, 21, 22, 24, 27, 30, 33, 35, 38, 42, 43, 44, 46, 48, 51, 54, 56, 57, 59, 62, 66, 67, 69, 70, 75, 76, 77, 78, 83, 84, 86, 88, 91, 93, 94, 96, 99, 102, 105, 107, 108, 110, 114, 115, 118, 120, 123, 126, 129, 131, 132, 133, 134, 138, 139, 140, 141, 142 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
A002828(a(n)) = 3; A025427(a(n)) > 0. - Reinhard Zumkeller, Feb 26 2015
REFERENCES
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 311.
LINKS
Eric Weisstein's World of Mathematics, Square Number.
FORMULA
Legendre: a nonnegative integer is a sum of three (or fewer) squares iff it is not of the form 4^k m with m == 7 (mod 8).
MATHEMATICA
Select[Range[150], SquaresR[3, #]>0&&SquaresR[2, #]==0&] (* Harvey P. Dale, Nov 01 2011 *)
PROG
(Haskell)
a000419 n = a000419_list !! (n-1)
a000419_list = filter ((== 3) . a002828) [1..]
-- Reinhard Zumkeller, Feb 26 2015
(PARI) is(n)=my(f=factor(n)); for(i=1, #f[, 1], if(f[i, 2]%2 && f[i, 1]%4==3, return( n/4^valuation(n, 4)%8 !=7 ))); 0 \\ Charles R Greathouse IV, Feb 07 2017
(Python)
def aupto(lim):
squares = [k*k for k in range(1, int(lim**.5)+2) if k*k <= lim]
sum2sqs = set(a+b for i, a in enumerate(squares) for b in squares[i:])
sum3sqs = set(a+b for a in sum2sqs for b in squares)
return sorted(set(range(lim+1)) & (sum3sqs - sum2sqs - set(squares)))
print(aupto(142)) # Michael S. Branicky, Mar 06 2021
CROSSREFS
Sequence in context: A022155 A066157 A073159 * A353716 A178890 A332933
KEYWORD
nonn,nice,easy
AUTHOR
EXTENSIONS
More terms from Arlin Anderson (starship1(AT)gmail.com)
STATUS
approved

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Last modified March 29 06:15 EDT 2024. Contains 371265 sequences. (Running on oeis4.)