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A163830
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The n-th composite minus the product of the indices of the primes in its prime factorization.
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1
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3, 4, 7, 5, 7, 10, 10, 9, 15, 14, 17, 13, 17, 22, 16, 20, 19, 24, 24, 31, 23, 27, 23, 32, 30, 27, 37, 34, 39, 33, 37, 46, 33, 41, 37, 46, 46, 40, 52, 41, 48, 54, 51, 47, 63, 47, 56, 61, 51, 58, 68, 62, 57, 68, 57, 66, 77, 65, 69, 76, 64, 72, 67, 83, 78, 67, 83, 71, 79, 71, 94
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OFFSET
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1,1
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COMMENTS
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The product of the indices of the primes (counted with multiplicity) is represented by A003963. An intermediate sequence m-A003963(m) = 0, 1, 1, 3, 2, 4, 3, 7, 5, 7, 6, ... at m=1, 2, 3, ... is defined and evaluated where m=A002808(n) is composite.
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LINKS
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FORMULA
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EXAMPLE
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MAPLE
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A002808 := proc(n) local a; if n = 1 then 4; else for a from procname(n-1)+1 do if not isprime(a) then RETURN(a) ; end if; end do; end if; end proc:
A163829 := proc(n) local c; c := A002808(n) ; pfs := ifactors(c)[2] ; mul( numtheory[pi](op(1, p))^op(2, p), p=pfs) ; end:
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MATHEMATICA
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With[{nn=100}, #-Times@@(PrimePi/@Flatten[Table[#[[1]], {#[[2]]}]&/@ FactorInteger[#]])&/@Complement[Range[2, nn], Prime[Range[ PrimePi[ nn]]]]](* Harvey P. Dale, Mar 29 2012 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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