A163515 If n-th composite is the product of k1-th prime, k2-th prime, ..., kr-th prime then set a(n) = k1 + k2 + ... + kr.

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

Offset: 1

Author

Juri-Stepan Gerasimov, Jul 30 2009

Keywords

• nonn

Examples

			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.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A002808, A061395.

Programs

Maple

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

Mathematica

kp[c_]:=Total[Times@@@({PrimePi[#[[1]]],#[[2]]}&/@FactorInteger[c])]; kp/@Select[ Range[200],CompositeQ] (* Harvey P. Dale, Nov 03 2022 *)

Extensions

Corrected by R. J. Mathar, Aug 05 2009

Example edited by Harvey P. Dale, Nov 27 2013

Further edits by Jon E. Schoenfield, Mar 07 2019