A141276 a(n) = A338038(A002808(n)).

4, 5, 5, 5, 7, 7, 9, 8, 6, 7, 9, 10, 13, 8, 7, 15, 6, 11, 10, 7, 14, 19, 12, 9, 21, 16, 10, 12, 15, 10, 25, 9, 9, 9, 20, 17, 8, 16, 12, 22, 31, 12, 33, 12, 8, 18, 16, 21, 26, 14, 10, 39, 10, 23, 18, 18, 11, 7, 43, 14, 22, 45, 32, 16, 12, 20, 27, 34, 49, 24, 10, 11, 16, 11, 22, 18, 15, 55

Offset: 1

Author

Juri-Stepan Gerasimov, Aug 08 2008

Keywords

• nonn

Examples

			Let k(n) = n-th composite (A002808(n)). Then:
a(4)=5 because k(4) = 9 = 3^2 and 5=3+2;
a(9)=6 because k(9) = 16 = 2^4 and 6=2+4;
a(10)=7 because k(10) = 18 = 2*3^2 and 7=2+3+2.
		

Crossrefs

Cf. A002808, A338038.

Programs

Maple

A141276 := proc(n) local a, ifs, p, c ; if not isprime(n) then a := 0 ; ifs := ifactors(n)[2] ; for p in ifs do a := a + op(1,p) ; if op(2,p) > 1 then a := a+ op(2,p) ; fi; od: printf("%d,",a) ; end if; return ; end: for n from 4 to 200 do A141276(n); end do; # R. J. Mathar, Apr 28 2010

Mathematica

a[n_] := Plus @@ First /@ (f = FactorInteger[n]) + Plus @@ Select[Last /@ f, # > 1 &];a/@Select[Range[106], CompositeQ] (* James C. McMahon, Jul 19 2025 *)

Extensions

Entries checked by R. J. Mathar, Apr 28 2010

Edited (with clearer definition) by N. J. A. Sloane, Jun 15 2021