A243283 One more than the partial sums of the characteristic function of A070003.

1, 1, 1, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 16

Offset: 1

Author

Antti Karttunen, Jun 02 2014

Keywords

• nonn

Comments

a(n) tells how many positive integers <= n are divisible by the square of their largest noncomposite divisor. (This definition includes 1 as it is divisible by 1^2.)

a(n) = n - A243285(n).

a(1) = 1 and for all n > 1, a(A070003(n-1)) = n, thus this sequence works as an inverse function for the injection {a(1) = 1, a(n>1) = A070003(n-1)} (a sequence which is the union of {1} and A070003).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

One more than A243282.

Differs from A243284 for the first time at n=48. Here a(48)=10.

Cf. A070003, A102354, A243285, A057627.