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 A057627 Number of nonsquarefree numbers not exceeding n. 20
 0, 0, 0, 1, 1, 1, 1, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 7, 7, 7, 7, 8, 9, 9, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 16, 16, 16, 17, 18, 19, 19, 20, 20, 21, 21, 22, 22, 22, 22, 23, 23, 23, 24, 25, 25, 25, 25, 26, 26, 26, 26, 27, 27, 27, 28, 29, 29, 29 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 COMMENTS Number of integers k in A013929 in the range 1 <= k <= n. Asymptotic to k*n where k = 1 - 1/zeta(2) = 1 - 6/Pi^2 = A229099. - Daniel Forgues, Jan 28 2011 This sequence is the sequence of partial sums of A107078 (not of A056170). - Jason Kimberley, Feb 01 2017 Number of partitions of 2n into two parts with the smallest part nonsquarefree. - Wesley Ivan Hurt, Oct 25 2017 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 FORMULA a(n) = n - A013928(n+1) = n - Sum(Moebius(k)^2, k=1..n). G.f.: Sum_{k>=1} (1 - mu(k)^2)*x^k/(1 - x). - Ilya Gutkovskiy, Apr 17 2017 EXAMPLE a(36)=13 because 13 nonsquarefree numbers exist which do not exceed 36:{4,8,9,12,16,18,20,24,25,27,28,32,36}. This sequence is different from A013940, albeit the first 35 terms are identical. MAPLE N:= 1000: # to get terms up to a(N) B:= Array(1..N, numtheory:-issqrfree): C:= map(`if`, B, 0, 1): A:= map(round, Statistics:-CumulativeSum(C)): seq(A[n], n=1..N); # Robert Israel, Jun 03 2014 MATHEMATICA Accumulate[Table[If[SquareFreeQ[n], 0, 1], {n, 80}]] (* Harvey P. Dale, Jun 04 2014 *) PROG (Scheme) (define (A057627 n) (- n (A013928 (+ n 1)))) (PARI) a(n)=my(s); forprime(p=2, sqrtint(n), s+=n\p^2); s \\ Charles R Greathouse IV, May 18 2015 CROSSREFS Cf. A005117, A008683, A013929, A013940, A013928, A002321, A028442, A107078 , A229099, A294242. Sequence in context: A106742 A106733 A087838 * A013940 A029129 A087842 Adjacent sequences:  A057624 A057625 A057626 * A057628 A057629 A057630 KEYWORD nonn,easy AUTHOR Labos Elemer, Oct 10 2000 EXTENSIONS Offset and formula corrected by Antti Karttunen, Jun 03 2014 STATUS approved

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Last modified January 24 00:10 EST 2019. Contains 319404 sequences. (Running on oeis4.)