A131187 a(n) = the number of positive integers < n that are neither a divisor of n nor a divisor of (n+1).

0, 0, 0, 1, 1, 2, 3, 3, 4, 6, 5, 6, 9, 8, 8, 11, 11, 12, 13, 12, 15, 18, 15, 15, 20, 20, 19, 22, 21, 22, 25, 24, 27, 28, 24, 27, 33, 32, 29, 32, 33, 34, 37, 34, 37, 42, 37, 37, 42, 42, 43, 46, 45, 44, 45, 46, 51, 54, 47, 48, 57, 54, 52, 55, 55, 58, 61, 60, 59, 62, 59, 60, 69, 66

Offset: 1

Author

Leroy Quet, Sep 25 2007

Keywords

• nonn

Examples

			The divisors of 9 are 1,3,9. The divisors of 9+1=10 are 1,2,5,10. The 4 positive integers which are < 9 and are neither divisors of 9 nor of 10 are 4,6,7,8. So a(9) = 4.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A049820.

Programs

Maple

A131187 := proc(n) local divs ; divs := ( numtheory[divisors](n) union numtheory[divisors](n+1) ) minus {n,n+1} ; n-1-nops(divs) ; end: seq(A131187(n),n=1..80) ; # R. J. Mathar, Oct 28 2007

Mathematica

Table[d=Divisors[n];dn=Divisors[n+1];Length[Complement[Range[n],Union[d,dn]]],{n,74}] (* James C. McMahon, Feb 17 2025 *)

PARI

a(n) = n + 2 - numdiv(n) - numdiv(n+1); \\ Michel Marcus, Feb 17 2025

Formula

a(n) = n + 2 - d(n) - d(n+1), where d(n) is the number of positive divisors of n.

Extensions

More terms from R. J. Mathar, Oct 28 2007