A243282 - OEIS

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

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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