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a(1)=1, a(n) = n + (sum of distinct primes dividing a(n-1)).
1

%I #7 Mar 11 2015 17:44:00

%S 1,2,5,9,8,8,9,11,20,17,28,21,23,37,52,31,48,23,42,32,23,45,31,55,41,

%T 67,94,77,47,77,49,39,49,41,76,57,59,97,136,59,100,49,50,51,65,64,49,

%U 55,65,68,70,66,69,80,62,89,146,133,85,82,104,77,81,67,132,82,110,86,114,94

%N a(1)=1, a(n) = n + (sum of distinct primes dividing a(n-1)).

%H Harvey P. Dale, <a href="/A111290/b111290.txt">Table of n, a(n) for n = 1..1000</a>

%e a(10) = 10 + (sum of distinct primes dividing 20) = 10 + 2 + 5 = 17.

%t nxt[{n_,a_}]:={n+1,n+1+Total[Transpose[FactorInteger[a]][[1]]]}; Join[{1}, Transpose[ NestList[nxt,{2,2},70]][[2]]] (* _Harvey P. Dale_, Mar 11 2015 *)

%o (PARI) b=1;for(i=2,100,v=factor(b);b=i+sum(j=1,matsize(v)[1],v[j,1]);print1(b,",")) (Klasen)

%K nonn

%O 1,2

%A _Leroy Quet_, Nov 01 2005

%E More terms from Lambert Klasen (lambert.klasen(AT)gmx.net), Nov 06 2005