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Search: id:A078910
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| A078910 |
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Let r+i*s be the sum of the distinct first-quadrant Gaussian integers dividing n; sequence gives r values. |
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+0
5
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| 1, 4, 4, 10, 9, 16, 8, 22, 13, 37, 12, 40, 19, 32, 36, 46, 23, 52, 20, 93, 32, 48, 24, 88, 56, 77, 40, 80, 37, 148, 32, 94, 48, 95, 72, 130, 45, 80, 76, 205, 51, 128, 44, 120, 117, 96, 48, 184, 57, 231, 92, 193, 63, 160, 108, 176, 80, 151, 60, 372, 73, 128, 104, 190, 176
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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(n) = A078911(n)+A000203(n). - Vladeta Jovovic (vladeta(AT)eunet.rs), 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) = 10.
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PROGRAM
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(PARI) A078910(n, S=[])=sigma(n)+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 (Maximilian.Hasler(AT)gmail.com), Nov 22 2007
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CROSSREFS
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Cf. A078911, A078458, A078908, A078909.
Cf. A078930.
Sequence in context: A007426 A050348 A134637 this_sequence A140234 A167132 A101256
Adjacent sequences: A078907 A078908 A078909 this_sequence A078911 A078912 A078913
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jan 11 2003
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 11 2003
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