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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 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

If n has repeated prime factors, then these are added as indicated by the exponents. For example, 18540 = 2^5 * 3 * 191, therefore we add 2 five times in our sum to obtain the next term of the sequence. - From 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). M. F. Hasler, Jul 18 2011

STATUS

approved

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Last modified November 21 05:01 EST 2017. Contains 294988 sequences.