A192896 a(n+1) is the sum of a(n) and the prime factors of a(n), counted with multiplicity. Start with a(0) = 3.

3, 6, 11, 22, 35, 47, 94, 143, 167, 334, 503, 1006, 1511, 3022, 4535, 5447, 5879, 11758, 17639, 18239, 18336, 18540, 18658, 19170, 19257, 19405, 23291, 46582, 69875, 69946, 70842, 82654, 82714, 124073, 126467, 137975

Offset

0,1

Comments

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

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

a(n+1) = A075254(a(n)). - Robert Israel, Nov 02 2025

Example

For n = 3, n is a prime number so the next term is 6.
For n = 6, n is not a prime factor, as n = 2*3, so the next term = 6+2+3 = 11.

Maple

f:= proc(n) local t; n + add(t[1]*t[2], t=ifactors(n)[2]) end proc:
R:= 3: x:= 3:
for i from 1 to 50 do x:= f(x); R:= R, x od:
R; # Robert Israel, Nov 02 2025

Mathematica

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 *)

Prog

(PARI) A192896(n, m=3) = { for(i=1, n, m+=A001414(m)); m } \\ M. F. Hasler, Jul 18 2011

Crossrefs

Cf. A096461, similar but starting with 2 rather than 3. See also A001414. Cf. A075254.

Sequence in context: A104253 A283668 A191581 * A115030 A228206 A195734

Adjacent sequences: A192893 A192894 A192895 * A192897 A192898 A192899

Keyword

nonn

Author

Lawrence Hollom, Jul 12 2011

Extensions

More terms from Vincenzo Librandi and Alonso del Arte, Jul 12 2011

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

Definition clarified by Robert Israel, Nov 02 2025

Status

approved