A244259 Number of non-twin isolated divisors of n.

1, 0, 0, 0, 2, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2, 2, 3, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 2, 2, 4, 2, 2, 2, 2, 2, 3, 2, 3, 3, 2, 2, 4, 3, 4, 2, 3, 2, 5, 4, 3, 2, 2, 2, 4, 2, 2, 2, 4, 4, 5, 2, 3, 2, 4, 2, 5, 2, 2, 3, 3, 4, 5, 2, 4, 3, 2, 2, 4, 4, 2, 2, 5, 2, 5, 4, 3, 2, 2, 4, 6

Offset: 1

Author

Juri-Stepan Gerasimov, Jun 24 2014

Keywords

• nonn
• easy

Comments

Number of divisors d of n such that neither the positive values d - 2 nor d - 1 nor d + 1 nor d + 2 divide n.

An isolated divisor d is non-twin if neither the positive values d - 2 nor d + 2 divide n.

Examples

			The isolated divisors of 56 are: 4, 14, 28, 56. The non-twin divisors of 56 are: 1, 7, 8, 14, 28, 56. The non-twin isolated divisors of 56 are therefore 14, 28, 56. There are 3 of these, so a(56) = 3.
		

Links

• Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A132881 (number of isolated divisors of n), A243917 (number of non-twin divisors of n).

Programs

PARI

a(n) = sumdiv(n, d, (((d<=2) || (n % (d-2))) && ((d<=1) || (n % (d-1))) && (n % (d+1)) && (n % (d+2)))); \\ Michel Marcus, Jun 25 2014