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A243283 One more than the partial sums of the characteristic function of A070003. 5
1, 1, 1, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 16 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

a(n) tells how many natural numbers <= n there are which are divisible by the square of their largest noncomposite divisor. (This definition includes 1 as it is divisible by 1^2).

a(n) = n - A243285(n).

a(1)=1 and for all n>1, a(A070003(n-1)) = n, thus this sequence works as an inverse function for the injection {a(1)=1, a(n>1)=A070003(n-1)} (a sequence which is an union of {1} and A070003).

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

PROG

(Scheme, with memoizing macro definec from Antti Karttunen's IntSeq-library)

(definec (A243283 n) (if (<= n 1) n (+ (A243283 (- n 1)) (if (zero? (A241917 n)) 1 0))))

CROSSREFS

One more than A243282.

Differs from A243284 for the first time at n=48. Here a(48)=10.

Cf. A070003, A102354, A243285, A057627.

Sequence in context: A069623 A076411 A217038 * A243284 A072613 A029551

Adjacent sequences:  A243280 A243281 A243282 * A243284 A243285 A243286

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jun 02 2014

STATUS

approved

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Last modified May 26 07:44 EDT 2019. Contains 323579 sequences. (Running on oeis4.)