A243282 Partial sums of the characteristic function for A070003.

0, 0, 0, 1, 1, 1, 1, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 15, 15, 15, 15, 15, 15, 16

Offset: 1

Author

Antti Karttunen, Jun 02 2014

Keywords

• nonn

Comments

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.

Examples

			A070003(402) = 10000, thus a(10000) = 402.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

One less than A243283.

Cf. A070003, A243285.

Programs

Mathematica

Accumulate[Join[{0},Table[If[Divisible[n,Last[Select[Divisors[n],PrimeQ]]^2],1,0],{n,2,90}]]] (* Harvey P. Dale, Sep 05 2018 *)

Formula

a(n) = A243283(n)-1.