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

1,4

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

Prog

(Scheme, with memoizing macro definec from Antti Karttunen's IntSeq-library)
(definec (A243283 n) (if (<= n 1) n (+ (A243283 (- n 1)) (if (zero? (A241917 n)) 1 0))))

Crossrefs

One more than A243282.

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

Cf. A070003, A102354, A243285, A057627.

Sequence in context: A076411 A217038 A309196 * A243284 A338623 A072613

Adjacent sequences: A243280 A243281 A243282 * A243284 A243285 A243286

Keyword

nonn

Author

Antti Karttunen, Jun 02 2014

Status

approved