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A192896 Prime factor addition sequence: For the term n, add all the prime factors of n to n. If n is a prime then add n to it. Start with n = 3.

%I A192896 #36 Jun 02 2025 04:14:30
%S A192896 3,6,11,22,35,47,94,143,167,334,503,1006,1511,3022,4535,5447,5879,
%T A192896 11758,17639,18239,18336,18540,18658,19170,19257,19405,23291,46582,
%U A192896 69875,69946,70842,82654,82714,124073,126467,137975
%N A192896 Prime factor addition sequence: For the term n, add all the prime factors of n to n. If n is a prime then add n to it. Start with n = 3.
%C A192896 If n has repeated prime factors, then these are added as indicated by the exponents. For example, 18336 = 2^5 * 3 * 191, therefore we add 2 five times in our sum to obtain the next term of the sequence. - _Alonso del Arte_, Jul 12 2011
%H A192896 G. C. Greubel, <a href="/A192896/b192896.txt">Table of n, a(n) for n = 0..1000</a>
%e A192896 For n = 3, n is a prime number so the next term is 6.
%e A192896 For n = 6, n is not a prime factor, as n = 2*3, so the next term = 6+2+3 = 11.
%t A192896 a[1] := 3; a[n_] := a[n] = a[n - 1] + Plus@@Times@@@FactorInteger@a[n - 1]; Table[a[n], {n, 40}] (* _Alonso del Arte_, Jul 12 2011 *)
%o A192896 (PARI) A192896(n,m=3) = { for(i=1,n, m+=A001414(m)); m } \\ _M. F. Hasler_, Jul 18 2011
%Y A192896 Cf. A096461, similar but starting with 2 rather than 3. See also A001414.
%K A192896 nonn
%O A192896 0,1
%A A192896 _Lawrence Hollom_, Jul 12 2011
%E A192896 More terms from _Vincenzo Librandi_ and _Alonso del Arte_, Jul 12 2011
%E A192896 Offset corrected to 0 (so as to have a(n) = n times iterated A001414 acting on the initial value) by _M. F. Hasler_, Jul 18 2011