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A078911
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Let r+i*s be the sum of the distinct first-quadrant Gaussian integers dividing n; sequence gives s values.
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7
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0, 1, 0, 3, 3, 4, 0, 7, 0, 19, 0, 12, 5, 8, 12, 15, 5, 13, 0, 51, 0, 12, 0, 28, 25, 35, 0, 24, 7, 76, 0, 31, 0, 41, 24, 39, 7, 20, 20, 115, 9, 32, 0, 36, 39, 24, 0, 60, 0, 138, 20, 95, 9, 40, 36, 56, 0, 61, 0, 204, 11, 32, 0, 63, 92, 48, 0, 113, 0, 152, 0, 91, 11, 71, 100, 60, 0, 140
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OFFSET
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1,4
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COMMENTS
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A Gaussian integer z = x+iy is in the first quadrant if x > 0, y >= 0. Just one of the 4 associates z, -z, i*z, -i*z is in the first quadrant.
a(A004614(n)) = 0; a(n) = A078910(n)-A000203(n). - Vladeta Jovovic, Jan 11 2003
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LINKS
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M. F. Hasler, Table of n, a(n) for n = 1..1000.
Michael Somos, PARI program for finding prime decomposition of Gaussian integers
Index entries for Gaussian integers and primes
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EXAMPLE
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The distinct first-quadrant divisors of 4 are 1, 1+i, 2, 2+2*i, 4, with sum 10+3*i, so a(4) = 3.
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MATHEMATICA
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Table[Re[Plus@@Divisors[n, GaussianIntegers -> True]], {n, 65}] (* Alonso del Arte, Jan 24 2012 *)
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PROG
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(PARI) A078911(n, S=[])=sumdiv(n*I, d, if(real(d)&imag(d)&!setsearch(S, d=vecsort(abs([real(d), imag(d)]))), S=setunion(S, [d]); (d[1]+d[2])>>(d[1]==d[2]))) - M. F. Hasler, Nov 22 2007
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CROSSREFS
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Cf. A078910, A078458, A078908, A078909, A078930.
Sequence in context: A230811 A117032 A243823 * A082899 A249491 A245250
Adjacent sequences: A078908 A078909 A078910 * A078912 A078913 A078914
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Jan 11 2003
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EXTENSIONS
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More terms from Vladeta Jovovic, Jan 11 2003
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STATUS
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approved
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