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A092695 Number of positive integers less than or equal to n which are not divisible by the primes 2,3,5,7. 8
0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,12

COMMENTS

This sequence is a special case of the following: Take different primes p_1, p_2,...,p_k. For a nonempty subset I of {1,2,...,k} denote by |I| the number of its elements. For a positive integer n denote A(n,I) = floor(n/product(p_i, i in I)). Then the number of positive integers m<=n such that m is divisible by none of p_1,p_2,...,p_k is equal n+sum((-1)^(|I|))A(n,I), where I runs over all nonempty subsets of {1,2,...,k}. - Milan Janjic, Apr 23 2007

REFERENCES

J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 62.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Index entries for two-way infinite sequences

FORMULA

G.f.: (x * P172 * P36) / (e(1) * e(210)) where e(n) = 1 - x^n, P36 = e(16) * e(20) * e(24) / (e(6) * e(8) * e(10)) is a polynomial of degree 36 and P172 is a polynomial of degree 172.

a(n + 210) = a(n) + 48. a(n) = -a(-1 - n).

EXAMPLE

x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10 + 2*x^11 + ...

PROG

(PARI) {a(n) = n - n\2 - n\3 - n\5 - n\7 + n\6 + n\10 + n\14 + n\15 + n\21 - n\30 + n\35 - n\42 - n\70 - n\105 + n\210}

(PARI) {a(n) = if( n<0, -a(-1 - n), sum( k=0, n, 1==gcd( k, 210)))}

(Haskell)

a092695 n = a092695_list !! n

a092695_list = scanl (+) 0 $

               map (fromEnum . (> 7)) (8 : tail a020639_list)

-- Reinhard Zumkeller, Mar 26 2012

CROSSREFS

Cf. A020639, A008364.

Sequence in context: A074198 A196169 A048688 * A281687 A033270 A285507

Adjacent sequences:  A092692 A092693 A092694 * A092696 A092697 A092698

KEYWORD

nonn

AUTHOR

Michael Somos, Mar 04 2004

STATUS

approved

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Last modified April 23 06:08 EDT 2019. Contains 322381 sequences. (Running on oeis4.)