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A243282 Partial sums of the characteristic function for A070003. 5
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 (list; graph; refs; listen; history; text; internal format)
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: A237115 A069637 A072292 * A093390 A025789 A080585

Adjacent sequences:  A243279 A243280 A243281 * A243283 A243284 A243285

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jun 02 2014

STATUS

approved

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Last modified October 23 16:46 EDT 2019. Contains 328373 sequences. (Running on oeis4.)