A144586 a(n) = odd and nonprime sum (with multiplicity) of prime factors of composite(k) = A002808(k).

9, 9, 9, 15, 9, 21, 15, 25, 33, 21, 39, 45, 27, 49, 15, 55, 15, 33, 63, 35, 15, 15, 69, 75, 15, 25, 81, 15, 45, 85, 25, 91, 15, 51, 15, 99, 21, 105, 21, 57, 15, 111, 115, 21, 35, 21, 63, 15, 65, 129, 25, 35, 133, 25, 21, 141, 75, 27, 77, 153, 27, 25, 159, 165, 21, 87, 169, 27

Offset: 1

Author

Juri-Stepan Gerasimov, Jan 04 2009

Keywords

• nonn

Examples

			At k=7, A002808(k) = 14 = 2*7, and 2 + 7 = 9 (an odd nonprime), and k=7 is the smallest index for which this occurs, so a(1)=9.
At k=11, A002808(k) = 20 = 2*2*5, and 2 + 2 + 5 = 9 (an odd nonprime), and k=11 is the 2nd smallest index for which this occurs, so a(2)=9.
At k=14, A002808(k) = 24 = 2*2*2*3, and 2 + 2 + 2 + 3 = 9 (an odd nonprime), and k=24 is the 3rd smallest index for which this occurs, so a(3)=9.
At k=16, A002808(k) = 26 = 2*13 and 2 + 13 = 15 (an odd nonprime), and k=26 is the 4th smallest index for which this occurs, so a(4)=15, etc.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002808, A046343, A141468.

Programs

Maple

pss := proc(n) a := 0 ; for d in ifactors(n)[2] do a := a+ op(2,d)*op(1,d) ; end do: a ; end proc:
A002808 := proc(n) 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:
A046343 := proc(n) pss(A002808(n)) ; end proc:
for k from 1 to 800 do a := A046343(k) ; if not isprime(a) and type(a,'odd') then printf("%d,",a) ; end if; end do: # R. J. Mathar, May 01 2010

Mathematica

Select[Map[Total[Times @@@ FactorInteger[#]] &, Range[500]], OddQ[#] && CompositeQ[#] &] (* Paolo Xausa, Aug 01 2025 *)

Extensions

Corrected at two or more places and extended by R. J. Mathar, May 01 2010

Example section edited by Jon E. Schoenfield, Oct 18 2015