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 A071010 Sigma(k)/4 when k is not a sum of 2 squares. 1
 1, 3, 2, 3, 7, 6, 6, 5, 8, 9, 6, 15, 10, 14, 18, 8, 12, 12, 15, 14, 24, 11, 21, 18, 12, 31, 18, 30, 18, 30, 20, 15, 42, 24, 26, 36, 17, 24, 36, 18, 31, 35, 24, 42, 20, 21, 56, 33, 30, 45, 28, 42, 32, 36, 30, 63, 39, 54, 26, 48, 27, 70, 54, 38, 62, 60, 36, 45, 36, 90, 42, 56, 78 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Conjecture : if n is not the sum of 2 squares sigma(n) == 0 (mod 4) (converse is not true : if sigma(n) == 0 (mod 4), n is sometimes the sum of 2 squares : sigma(65) = 84 == 0 (mod 4) but 65 = 49+16 is a sum of 2 squares). LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 FORMULA a(n) = sigma(A022544(n))/4. MATHEMATICA DivisorSigma[1, Select[Range[120], SquaresR[2, #] == 0 &]]/4  (* Amiram Eldar, May 13 2022 *) PROG (PARI) for(n=0, 200, if(sum(i=0, n, sum(j=0, i, if(i^2+j^2-n, 0, 1)))==0, print1(sigma(n)/4, ", "))) CROSSREFS Cf. A000203, A022544. Sequence in context: A332057 A275330 A141863 * A343231 A215934 A323895 Adjacent sequences:  A071007 A071008 A071009 * A071011 A071012 A071013 KEYWORD easy,nonn AUTHOR Benoit Cloitre, May 19 2002 STATUS approved

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Last modified August 12 07:10 EDT 2022. Contains 356067 sequences. (Running on oeis4.)