A058838 a(n) = 1 + sum of the anti-divisors of n.

1, 1, 3, 4, 6, 5, 11, 9, 9, 15, 13, 14, 20, 17, 19, 15, 29, 29, 19, 25, 23, 37, 35, 24, 40, 25, 43, 47, 25, 37, 43, 59, 49, 31, 53, 33, 51, 71, 53, 56, 42, 67, 57, 41, 87, 59, 61, 57, 73, 81, 43, 95, 89, 53, 75, 57, 75, 97, 91, 108, 58, 79, 113, 47, 85

Offset: 1

Author

Jon Perry, Dec 28 2001

Keywords

• nonn

Comments

See A066272 for definition of anti-divisor.

Examples

			Consider n = 18: 2n-1, 2n, 2n+1 are 35, 36, 37 with odd divisors > 1 {5,7,35}, {3,9}, {37} respectively and quotients {7, 5, 1}, {12, 4}, {1}; so the anti-divisors of 18 are 4, 5, 7, 12. Therefore a(18) = 1 + 28 = 29.
		

Links

• Jon Perry, Anti-divisors [Broken link]
• Jon Perry, The Anti-divisor [Cached copy]
• Jon Perry, The Anti-divisor: Even More Anti-Divisors [Cached copy]

Crossrefs

Cf. A066417, A066241, A066452.

Formula

a(n) = A066417(n) + 1.