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Search: id:A092695
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| A092695 |
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Number of positive integers less than or equal to n which are not divisible by the primes 2,3,5,7. |
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+0
7
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| 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; listen)
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OFFSET
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0,12
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COMMENT
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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 R. Janjic (agnus(AT)blic.net), Apr 23 2007
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REFERENCES
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J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 62.
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FORMULA
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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).
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PROGRAM
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(PARI) a(n)=n-n\2-n\3-n\5-n\7+n\6+n\10+n\14+n\15+n\21+n\35-n\30-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)))
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CROSSREFS
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Sequence in context: A114214 A074198 A048688 this_sequence A033270 A103264 A060960
Adjacent sequences: A092692 A092693 A092694 this_sequence A092696 A092697 A092698
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Mar 04 2004
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