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A053144
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Cototient of n-th primorial number.
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1
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1, 4, 22, 162, 1830, 24270, 418350, 8040810, 186597510, 5447823150, 169904387730, 6317118448410, 260105476071210, 11228680258518030, 529602053223499410, 28154196550210460730, 1665532558389396767070
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n)>A005367(n), a(n)>A002110(n)/2
As n-> Infinity, a(n)/A002110(n) = 1 because (in the limit) the quotient is the probability that a randomly selected integer contains at least one of the first n primes in its factorization. [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Apr 08 2010]
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FORMULA
| a(n)=A051593[A002110(n)]=A002110(n)-A005867(n)
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EXAMPLE
| In the reduced residue system of q(4)=2*3*5*7-210 the number of coprimes to 210 is 48, while a(4)=210-48=162 is the number values divisible with one of the prime factors of q(4).
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MATHEMATICA
| Abs[Table[ Total[Table[(-1)^(k + 1)* Total[Apply[Times, Subsets[Table[Prime[n], {n, 1, m}], {k}], 2]], {k, 0, m - 1}]], {m, 1, 22}]] [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Apr 08 2010]
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CROSSREFS
| A002110, A051593.
Sequence in context: A087547 A184942 A000779 * A089464 A111343 A187123
Adjacent sequences: A053141 A053142 A053143 * A053145 A053146 A053147
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Feb 28 2000
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