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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

%I #34 Jan 11 2019 20:37:40

%S 3,6,11,22,35,47,94,143,167,334,503,1006,1511,3022,4535,5447,5879,

%T 11758,17639,18239,18336,18540,18658,19170,19257,19405,23291,46582,

%U 69875,69946,70842,82654,82714,124073,126467,137975

%N 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 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 G. C. Greubel, <a href="/A192896/b192896.txt">Table of n, a(n) for n = 0..1000</a>

%e For n = 3, n is a prime number so the next term is 6.

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

%t 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 (PARI) A192896(n,m=3) = { for(i=1,n, m+=A001414(m)); m } \\ _M. F. Hasler_, Jul 18 2011

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

%K nonn

%O 0,1

%A _Lawrence Hollom_, Jul 12 2011

%E More terms from _Vincenzo Librandi_ and _Alonso del Arte_, Jul 12 2011

%E 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

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)