%I #11 Aug 04 2024 03:00:24
%S 242,213,3445,111,8718,5,2001,69,3526,299,1074,5,2222,537,9177,129,
%T 4114,5,8,598,7843,111,1235,10,2984,303,3538,417,987,7,1771,91,7659,
%U 57,9269,10,2264,145,1197,219,1606,5,1826,115,8897,203,618,5,8,159,2673,183
%N Least number k such that k, k+n, k+2*n and k+3*n have the same number of divisors.
%C Fourth row of A113465.
%H Amiram Eldar, <a href="/A113468/b113468.txt">Table of n, a(n) for n = 1..10000</a>
%e a(19) = 8 because 8, 8 + 19 = 27, 8 + 2*19 = 46 and 8 + 3*19 = 65 each have 4 divisors.
%t a[n_] := Module[{k = 1, d}, While[(d = DivisorSigma[0, k]) != DivisorSigma[0, k+n] || DivisorSigma[0, k+2*n] != d || DivisorSigma[0, k+3*n] != d, k++]; k]; Array[a, 60] (* _Amiram Eldar_, Aug 04 2024 *)
%o (PARI) a(n) = {my(k = 1, d); while((d = numdiv(k)) != numdiv(k+n) || numdiv(k+2*n) != d || numdiv(k+3*n) != d, k++); k;} \\ _Amiram Eldar_, Aug 04 2024
%Y Cf. A113465.
%K nonn
%O 1,1
%A _David Wasserman_, Jan 08 2006
%E Name corrected by _Amiram Eldar_, Aug 04 2024