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

0,4

Comments

a(n) = 0 for n from A033950.

Links

Table of n, a(n) for n=0..88.

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A033950.

Sequence in context: A199432 A073743 A021652 * A370427 A022961 A023447

Adjacent sequences: A360775 A360776 A360777 * A360779 A360780 A360781

Keyword

nonn

Author

Ctibor O. Zizka, Feb 20 2023

Status

approved