

A242493


a(n) is the number of notsqrtsmooth numbers ("jagged" numbers) not exceeding n. This is the counting function of A064052.


2



0, 1, 2, 2, 3, 4, 5, 5, 5, 6, 7, 7, 8, 9, 10, 10, 11, 11, 12, 13, 14, 15, 16, 16, 16, 17, 17, 18, 19, 19, 20, 20, 21, 22, 23, 23, 24, 25, 26, 26, 27, 28, 29, 30, 30, 31, 32, 32, 32, 32, 33, 34, 35, 35, 36, 36, 37, 38, 39, 39, 40, 41, 41, 41, 42, 43, 44, 45
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OFFSET

1,3


COMMENTS

This sequence is different from shifted A072490, after 22 terms.


REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, chapter 2.21, p. 166.


LINKS

Table of n, a(n) for n=1..68.


FORMULA

From Ridouane Oudra, Nov 07 2019: (Start)
a(n) = Sum_{i=1..floor(sqrt(n))} (pi(floor(n/i))  pi(i)).
a(n) = Sum_{p<=sqrt(n)} (p1) + Sum_{sqrt(n)<p<=n} floor(n/p), where p is prime.
a(n) = n  A064775(n). (End)


MATHEMATICA

jaggedQ[n_] := jaggedQ[n] = (f = FactorInteger[n][[All, 1]]; s = Sqrt[n]; Count[f, p_ /; p > s] > 0); a[n_] := ( For[ cnt = 0; j = 2, j <= n, j++, If[jaggedQ[j], cnt++]]; cnt); Table[a[n], {n, 1, 100}]


CROSSREFS

Cf. A064052, A064775.
Sequence in context: A054633 A327982 A072490 * A261345 A243285 A085972
Adjacent sequences: A242490 A242491 A242492 * A242494 A242495 A242496


KEYWORD

nonn,changed


AUTHOR

JeanFrançois Alcover, May 16 2014


STATUS

approved



