cp's OEIS Frontend

a(n) tells how many natural numbers <= n there are which are not divisible by the square of their largest noncomposite divisor.

The largest noncomposite divisor of 1 is 1 itself, and 1 is divisible by 1^2, thus 1 is not included in the count, and a(1)=0.

The "largest noncomposite divisor" for any integer > 1 means the same thing as the largest prime divisor, and thus we are counting the terms of A102750 (Numbers n such that square of largest prime dividing n does not divide n).

Thus this is the partial sums of the characteric function for A102750.

a(n) tells how many natural numbers <= n there are which are divisible by the square of their largest prime divisor. (This definition excludes 1 as it has no prime divisors.)

For all n, a(A070003(n)) = n, thus this sequence works also as an inverse function for the injection A070003.

a(n) = the number of distinct ways of writing such products m = k^2 * j, 0 < j <= k, (j and k natural numbers) that m is in range [1,n].

Different ways to write product for the same m are counted separately, e.g. for 64, both 8^2 * 1 and 4^2 * 4 are counted, so a(64) = a(63)+2 = 13+2 = 15.

Differs from A243283 for the first time at n=48, where a(48)=11, while A243283(48)=10. This is because 48 = 2*2*2*2*3 is the first integer which can be represented in the form k^2 * j, 0 < j <= k (namely as 48 = 4^2 * 3), even though it is not a member of A070003.