login
a(n) = the number of positive integers < n that are neither a divisor of n nor a divisor of (n+1).
2

%I #8 Aug 24 2015 02:26:55

%S 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,

%T 21,22,25,24,27,28,24,27,33,32,29,32,33,34,37,34,37,42,37,37,42,42,43,

%U 46,45,44,45,46,51,54,47,48,57,54,52,55,55,58,61,60,59,62,59,60,69,66

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

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

%e 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.

%p 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

%Y Cf. A049820.

%K nonn

%O 1,6

%A _Leroy Quet_, Sep 25 2007

%E More terms from _R. J. Mathar_, Oct 28 2007