A360778 - OEIS

%I #12 Mar 05 2023 17:08:35

%S 1,0,0,5,4,3,2,1,0,0,2,1,0,5,4,3,2,1,0,5,4,3,2,1,0,11,10,9,8,7,6,5,4,

%T 3,2,1,0,3,2,1,0,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,3,2,1,0,11,10,

%U 9,8,7,6,5,4,3,2,1,0,7,6,5,4,3,2,1,0,3,2,1,0,3,2,1,0

%N Smallest number k such that n + k is a refactorable number.

%C a(n) = 0 for n from A033950.

%e a(0) = 1 because 0 + 1 = 1, the next higher refactorable number.

%e a(1) = 0 because 1 is refactorable number.

%e a(2) = 0 because 2 is refactorable number.

%e a(3) = 5 because 3 + 5 = 8, the next higher refactorable number.

%e and so on.

%t a[n_] := Module[{m = n}, While[! Divisible[m, DivisorSigma[0, m]], m++]; m - n]; a[0] = 1; Array[a, 100, 0] (* _Amiram Eldar_, Feb 20 2023 *)

%o (PARI) a(n) = if (n==0, 1, my(k=0); while ((n+k) % numdiv(n+k), k++); k); \\ _Michel Marcus_, Feb 20 2023

%Y Cf. A033950.

%K nonn

%O 0,4

%A _Ctibor O. Zizka_, Feb 20 2023