

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


2



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
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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

Table of n, a(n) for n=0..35.


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


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.
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
Corrected offset to 0 (as to have a(n) = n times iterated A001414 acting on the initial value) by M. F. Hasler, Jul 18 2011


STATUS

approved



