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%I #12 Sep 04 2016 00:06:04
%S 1,17,89,79,321,49,23,20,139,87,26,48,41,56,75,88,38,81,49,134,196,78,
%T 68,114,155,65,552,111,80,349,103,104,142,192,110,342,123,359,395,249,
%U 83,349,101,74,481,292,219,1110,189,128,309,243,224,629,356,170,208
%N Least number k such that sigma(Sum_{j=0..n}{k-j}) = sigma(Sum_{j=0..n}{k+j}).
%H Paolo P. Lava, <a href="/A276318/b276318.txt">Table of n, a(n) for n = 0..1000</a>
%F Solutions of the equation sigma((n+1)*(2*k-n)/2) = sigma((n+1)*(2*k+n)/2).
%e a(3) = 79 because sigma(76+77+78+79) = sigma(79+80+81+82) = 576.
%p with(numtheory): P:= proc(q) local k,n; print(1);
%p for n from 1 to q do for k from n to q do
%p if sigma((n+1)*(2*k-n)/2)=sigma((n+1)*(2*k+n)/2)
%p then print(k); break; fi; od; od; end: P(10^9);
%t Table[k = n; While[DivisorSigma[1, Sum[k - j, {j, 0, n}]] != DivisorSigma[1, Sum[k + j, {j, 0, n}]], k++]; k, {n, 0, 56}] (* _Michael De Vlieger_, Aug 30 2016 *)
%o (PARI) a(n) = {if (n==0, k = 1, k = n); while (sigma((n+1)*(2*k-n)/2) != sigma((n+1)*(2*k+n)/2), k++); k;}
%Y Cf. A000203, A276319, A276320.
%K nonn,easy
%O 0,2
%A _Paolo P. Lava_, Aug 30 2016
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