A268868 a(n) is the sum of the prime factors (with repetition) of the sum of the preceding terms; a(1)=a(2)=1.

1, 1, 2, 4, 6, 9, 23, 25, 71, 73, 48, 263, 265, 120, 911, 913, 552, 192, 85, 27, 35, 53, 296, 66, 455, 289, 48, 188, 5021, 5023, 159, 190, 379, 946, 900, 600, 97, 204, 118, 512, 87, 148, 3886, 23291, 23293, 71, 896, 11812, 60, 41359, 2394, 11508, 5529, 8977, 200

Offset

1,3

Links

Paolo P. Lava, Table of n, a(n) for n = 1..2000

Formula

a(n) = A001414(A096461(n-1)); n>=3. - David James Sycamore, Mar 11 2018

Example

a(3) = 2 since the sum of all previous terms is 2 and the sum of prime factors of 2 with multiplicity is 2.
a(4) = 4 since the sum of all previous terms is 4 = 2 * 2; the sum of these factors is 4.
a(5) = 6 since the sum of all previous terms is 8 = 2 * 2 * 2; the sum of these factors is 6.
a(6) = 9 since the sum of all previous terms is 14 = 2 * 7. The sum of these factors is 9.
a(7) = 23 since the sum of all previous terms is the prime 23, etc.

Maple

A268868 := proc(n)
    option remember;
    if n <= 2 then
        1;
    else
        A001414(add(procname(i), i=1..n-1)) ;
    end if;
end proc: # R. J. Mathar, May 06 2016

Mathematica

a = {1, 1}; Do[AppendTo[a, Total@ Flatten@ Apply[Table[#1, {#2}] &, FactorInteger@ Total@ a, {1}]], {53}]; a (* Michael De Vlieger, Feb 15 2016 *)
Nest[Append[#, Total@ Flatten@ (ConstantArray@@@ FactorInteger@ Total@ #)] &, {1, 1}, 53] (* Michael De Vlieger, Mar 14 2018 *)

Prog

(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

Crossrefs

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

For records see A271927, A271928.

Cf. A096461.

Sequence in context: A079143 A192316 A049912 * A271927 A227526 A093081

Adjacent sequences: A268865 A268866 A268867 * A268869 A268870 A268871

Keyword

nonn

Author

David James Sycamore, Feb 15 2016

Extensions

Name edited and more terms from Michel Marcus, Feb 15 2016

Status

approved