A360778 Smallest number k such that n + k is a refactorable number.

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, 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, 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

Offset: 0

Author

Ctibor O. Zizka, Feb 20 2023

Keywords

• nonn

Comments

a(n) = 0 for n from A033950.

Examples

			a(0) = 1 because 0 + 1 = 1, the next higher refactorable number.
a(1) = 0 because 1 is refactorable number.
a(2) = 0 because 2 is refactorable number.
a(3) = 5 because 3 + 5 = 8, the next higher refactorable number.
and so on.
		

Crossrefs

Cf. A033950.

Programs

Mathematica

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 *)

PARI

a(n) = if (n==0, 1, my(k=0); while ((n+k) % numdiv(n+k), k++); k); \\ Michel Marcus, Feb 20 2023