A282255 Least k > 0 such that sigma(n) divides sigma(n+k).

1, 3, 3, 8, 1, 5, 7, 16, 9, 7, 3, 16, 7, 1, 8, 9, 5, 27, 5, 6, 10, 8, 7, 14, 23, 15, 27, 11, 9, 16, 11, 36, 2, 19, 7, 81, 37, 16, 21, 18, 3, 20, 43, 16, 45, 5, 15, 27, 25, 30, 4, 45, 32, 2, 11, 31, 22, 30, 28, 18, 14, 7, 40, 128, 13, 4, 67, 14, 8, 24, 23, 189, 73, 39, 37, 32, 28, 14, 35, 42, 81, 14, 9, 40, 17, 45

Offset: 1

Author

Altug Alkan, Feb 10 2017

Keywords

• nonn

Examples

			a(4) = 8 because sigma(4) = 7 divides sigma(4 + 8) = 28 and 8 is the least positive number with this property.
		

Links

• Altug Alkan, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A069789.

Programs

Mathematica

Table[k = 1; While[! Divisible[DivisorSigma[1, n + k], DivisorSigma[1, n]], k++]; k, {n, 120}] (* Michael De Vlieger, Feb 10 2017 *)

PARI

a(n) = my(k = 1); while (sigma(n+k) % sigma(n) != 0, k++); k;

Formula

a(n) = A069789(n) - n. - Michel Marcus, Feb 10 2017