A243283 - OEIS

%I #18 Jul 18 2022 22:48:32

%S 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,

%T 9,10,10,10,10,10,10,10,10,10,10,10,10,10,11,12,12,12,12,13,13,13,13,

%U 13,13,13,13,13,13,14,14,14,14,14,14,14,14,15,15,15,16

%N One more than the partial sums of the characteristic function of A070003.

%C 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.)

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

%C 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).

%H Antti Karttunen, <a href="/A243283/b243283.txt">Table of n, a(n) for n = 1..10000</a>

%o (Scheme, with memoizing macro definec from _Antti Karttunen_'s IntSeq-library)

%o (definec (A243283 n) (if (<= n 1) n (+ (A243283 (- n 1)) (if (zero? (A241917 n)) 1 0))))

%Y One more than A243282.

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

%Y Cf. A070003, A102354, A243285, A057627.

%K nonn

%O 1,4

%A _Antti Karttunen_, Jun 02 2014