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A163515
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If n-th composite is the product of k1-th prime, k2-th prime, ..., kr-th prime then set a(n) = k1 + k2 + ... + kr.
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3
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2, 3, 3, 4, 4, 4, 5, 5, 4, 5, 5, 6, 6, 5, 6, 7, 6, 6, 6, 5, 7, 8, 7, 6, 9, 8, 6, 7, 7, 7, 10, 6, 8, 7, 9, 8, 7, 8, 7, 10, 11, 7, 12, 8, 6, 9, 8, 9, 11, 8, 7, 13, 8, 10, 9, 9, 7, 8, 14, 8, 10, 15, 12, 8, 8, 10, 11, 13, 16, 11, 7, 9, 9, 8, 10, 9, 9, 17, 8, 9, 14, 8, 11, 12, 12, 10, 18, 11, 8, 10, 19, 15
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OFFSET
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1,1
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LINKS
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EXAMPLE
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The 1st composite is 4 = 2*2 = prime(1)*prime(1), so a(1) = 1 + 1 = 2;
the 2nd composite is 6 = 2*3 = prime(1)*prime(2), so a(2) = 1 + 2 = 3;
the 3rd composite is 8 = 2*2*2 = prime(1)*prime(1)*prime(1), so a(3) = 1 + 1 + 1 = 3;
the 4th composite is 9 = 3*3 = prime(2)*prime(2), so a(4) = 2 + 2 = 4.
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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: A163515 := proc(n) local c; c := A002808(n) ; pfs := ifactors(c)[2] ; add( op(2, p)*numtheory[pi](op(1, p)), p=pfs) ; end: seq(A163515(n), n=1..100) ; # R. J. Mathar, Aug 05 2009
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MATHEMATICA
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kp[c_]:=Total[Times@@@({PrimePi[#[[1]]], #[[2]]}&/@FactorInteger[c])]; kp/@Select[ Range[200], CompositeQ] (* Harvey P. Dale, Nov 03 2022 *)
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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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