A268868 - OEIS

%I #44 Mar 21 2018 06:43:16

%S 1,1,2,4,6,9,23,25,71,73,48,263,265,120,911,913,552,192,85,27,35,53,

%T 296,66,455,289,48,188,5021,5023,159,190,379,946,900,600,97,204,118,

%U 512,87,148,3886,23291,23293,71,896,11812,60,41359,2394,11508,5529,8977,200

%N a(n) is the sum of the prime factors (with repetition) of the sum of the preceding terms; a(1)=a(2)=1.

%H Paolo P. Lava, <a href="/A268868/b268868.txt">Table of n, a(n) for n = 1..2000</a>

%F a(n) = A001414(A096461(n-1)); n>=3. - _David James Sycamore_, Mar 11 2018

%e a(3) = 2 since the sum of all previous terms is 2 and the sum of prime factors of 2 with multiplicity is 2.

%e a(4) = 4 since the sum of all previous terms is 4 = 2 * 2; the sum of these factors is 4.

%e a(5) = 6 since the sum of all previous terms is 8 = 2 * 2 * 2; the sum of these factors is 6.

%e a(6) = 9 since the sum of all previous terms is 14 = 2 * 7. The sum of these factors is 9.

%e a(7) = 23 since the sum of all previous terms is the prime 23, etc.

%p A268868 := proc(n)

%p     option remember;

%p     if n <= 2 then

%p         1;

%p     else

%p         A001414(add(procname(i),i=1..n-1)) ;

%p     end if;

%p end proc: # _R. J. Mathar_, May 06 2016

%t a = {1, 1}; Do[AppendTo[a, Total@ Flatten@ Apply[Table[#1, {#2}] &, FactorInteger@ Total@ a, {1}]], {53}]; a (* _Michael De Vlieger_, Feb 15 2016 *)

%t Nest[Append[#, Total@ Flatten@ (ConstantArray@@@ FactorInteger@ Total@ #)] &, {1, 1}, 53] (* _Michael De Vlieger_, Mar 14 2018 *)

%o (PARI) lista(nn) = {va = vector(nn); print1(va[1] = 1, ", "); print1(va[2] = 1, ", "); sp = vecsum(va); for (k=3, nn, f = factor(sp); va[k] = sum(j=1, #f~, f[j,1]*f[j,2]); print1(va[k], ", "); sp += va[k];);} \\ _Michel Marcus_, Feb 15 2016

%Y Cf. A001414, A269004 (similar sequence with initial terms 1,2).

%Y For records see A271927, A271928.

%Y Cf. A096461.

%K nonn

%O 1,3

%A _David James Sycamore_, Feb 15 2016

%E Name edited and more terms from _Michel Marcus_, Feb 15 2016