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 A295084 Number of sqrt(n)-smooth numbers <= n. 3
 1, 1, 1, 3, 3, 3, 3, 4, 7, 7, 7, 8, 8, 8, 8, 9, 9, 10, 10, 10, 10, 10, 10, 11, 16, 16, 17, 17, 17, 18, 18, 19, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 21, 21, 22, 22, 22, 23, 30, 31, 31, 31, 31, 32, 32, 33, 33, 33, 33, 34, 34, 34, 35, 36, 36, 36, 36, 36, 36, 37, 37, 38, 38, 38, 39, 39, 39, 39, 39, 40 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS a(n) = number of positive integers m<=n such that A006530(m) <= sqrt(n). LINKS Wikipedia, Smooth number FORMULA a(n) = n - A241419(n). If n is in A063539, then a(n)=a(n-1)+1; if n is in A001248, i.e., n=p^2 for prime p, then a(n)=a(n-1)+p; otherwise a(n)=a(n-1). a(n) = (1 - log(2))*n + O(n/log(n)) as n -> infinity. - Robert Israel, Nov 14 2017 MAPLE N:= 100: # to get a(1)..a(N) G:= [0, seq(max(numtheory:-factorset(n)), n=2..N)]: seq(nops(select(t -> t^2 <= n, G[1..n])), n=1..N); # Robert Israel, Nov 14 2017 PROG (PARI) A295084(n) = my(r=n); forprime(p=sqrtint(n)+1, n, r-=n\p); r; CROSSREFS Cf. A048098 (indices of records), A063539, A241419. Sequence in context: A006671 A046074 A328914 * A068048 A176994 A264050 Adjacent sequences:  A295081 A295082 A295083 * A295085 A295086 A295087 KEYWORD nonn,look AUTHOR Max Alekseyev, Nov 13 2017 STATUS approved

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Last modified December 6 04:14 EST 2019. Contains 329784 sequences. (Running on oeis4.)