login
Least k such that sigma(k*n)/tau(k*n) = sigma(k*n+1)/tau(k*n+1), or 0 if no such k exists.
0

%I #39 Jul 28 2016 10:57:40

%S 5,7,895,1363,1,3353,2,2589,1007,10341,1265,1726,7,1,179,6634,10052,

%T 5745,86,53389,958,12165,58,863,649,250017,2395,6103,46,3447,2714,

%U 3317,8110,5026,22653,2812637,94,43,16795,58069,61693,479,38,52790,1437,29,74,2027510,122367,70545

%N Least k such that sigma(k*n)/tau(k*n) = sigma(k*n+1)/tau(k*n+1), or 0 if no such k exists.

%C Corresponding averages are 3, 6, 540, 840, 3, 2880, 6, 3240, 1170, 8640, 1596, 3240, 28, 6, 540, 9072, 15120, 8640, 330, 55440, 2880, 21924, 270, 3240, 1860, 875070, 7200, ...

%e a(13) = 7 because sigma(7*13)/tau(7*13) = sigma(7*13+1)/tau(7*13+1).

%t a[n_] := Block[{k=1}, While[! Equal @@ (DivisorSigma[1, n*k + {0,1}] / DivisorSigma[ 0, n*k + {0,1}]), k++]; k]; Array[a, 20] (* _Giovanni Resta_, Jul 28 2016 *)

%o (PARI) a(n) = {my(k=1); while (sigma(k*n)/numdiv(k*n) != sigma(k*n+1)/numdiv(k*n+1), k++); k; }

%Y Cf. A238380.

%K nonn

%O 1,1

%A _Altug Alkan_, Jul 28 2016