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User: Lawrence Hollom

Lawrence Hollom has authored 1 sequences.

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.

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

Lawrence Hollom, Jul 12 2011

nonn

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

			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.

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

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

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 *)

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

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

cp's OEIS Frontend

User: Lawrence Hollom

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.

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