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

1,8

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.

Links

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

Formula

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

Example

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

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 *)

Prog

(define (A243282 n) (- (A243283 n) 1))

Crossrefs

One less than A243283.

Cf. A070003, A243285.

Sequence in context: A362915 A069637 A072292 * A093390 A025789 A080585

Adjacent sequences: A243279 A243280 A243281 * A243283 A243284 A243285

Keyword

nonn

Author

Antti Karttunen, Jun 02 2014

Status

approved