cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A078910 Let r+i*s be the sum of the distinct first-quadrant Gaussian integers dividing n; sequence gives r values.

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%I A078910 #19 Jan 25 2021 10:26:56
%S A078910 1,4,4,10,9,16,8,22,13,37,12,40,19,32,36,46,23,52,20,93,32,48,24,88,
%T A078910 56,77,40,80,37,148,32,94,48,95,72,130,45,80,76,205,51,128,44,120,117,
%U A078910 96,48,184,57,231,92,193,63,160,108,176,80,151,60,372,73,128,104,190,176
%N A078910 Let r+i*s be the sum of the distinct first-quadrant Gaussian integers dividing n; sequence gives r values.
%C A078910 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.
%H A078910 M. F. Hasler, <a href="/A078910/b078910.txt">Table of n, a(n) for n = 1..1000</a>.
%H A078910 Michael Somos, <a href="/A078458/a078458.txt">PARI program for finding prime decomposition of Gaussian integers</a>
%H A078910 <a href="/index/Ga#gaussians">Index entries for Gaussian integers and primes</a>
%F A078910 a(n) = A078911(n)+A000203(n). - _Vladeta Jovovic_, Jan 11 2003
%e A078910 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.
%t A078910 Table[Re[Plus@@Divisors[n, GaussianIntegers -> True]], {n, 65}] (* _Alonso del Arte_, Jan 24 2012 *)
%o A078910 (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_, Nov 22 2007
%Y A078910 Cf. A000203, A078911, A078458, A078908, A078909, A078930.
%Y A078910 Cf. A062327 for the number of first quadrant divisors of n.
%K A078910 nonn,easy
%O A078910 1,2
%A A078910 _N. J. A. Sloane_, Jan 11 2003
%E A078910 More terms from _Vladeta Jovovic_, Jan 11 2003