A282795 Start with n. If n is 1 or a prime, stop. Otherwise, add the prime factors of n (with repetition) to n, and repeat until reaching a prime, when we stop. If no prime is ever reached, a(n) = -1.

1, 2, 3, 23, 5, 11, 7, 23, 23, 17, 11, 19, 13, 23, 23, 47, 17, 41, 19, 29, 31, 47, 23, 47, 47, 41, 71, 71, 29, 71, 31, 83, 47, 53, 47, 71, 37, 59, 71, 71, 41, 83, 43, 59, 167, 71, 47, 59, 149, 167, 71, 167, 53, 83, 71, 167, 79, 89, 59, 251, 61

Offset: 1

Author

Peter Weiss, Feb 21 2017

Keywords

• nonn

Comments

a(n) > 0 for every n up to at least 2000000. - Ivan N. Ianakiev, Feb 23 2017

Examples

			4 -> 4+2+2 = 8 -> 8+2+2+2 = 14 -> 14+2+7 = 23, prime, so a(4) = 23.
		

Links

• R. J. Mathar, Table of n, a(n) for n = 1..100000

Crossrefs

Cf. A016837, A037274 (home primes), A075254, A195264.

Programs

Maple

A282795 := proc(n)
    local nrec;
    nrec := n ;
    while not isprime(nrec) and nrec <> 1 do
        nrec := A075254(nrec) ;
    end do:
    nrec ;
end proc:
seq(A282795(n),n=1..90) ; # R. J. Mathar, Feb 23 2017

Mathematica

f[n_]:=n+Total[Replace[{a_,b_}->a*b]/@FactorInteger[n]];
a[1]=1;a[n_]:=If[PrimeQ[n],n,Last[NestWhileList[f,n,!PrimeQ[#]&]]];
Array[a,2000000] (* Ivan N. Ianakiev, Feb 23 2017 *)