A269004 a(n) is the sum of the prime factors, with repetition, of the sum of all preceding terms, with initial terms a(1)=1 and a(2)=2.

1, 2, 3, 5, 11, 13, 12, 47, 49, 24, 167, 169, 503, 505, 1511, 1513, 912, 432, 5879, 5881, 600, 97, 204, 118, 512, 87, 148, 3886, 23291, 23293, 71, 896, 11812, 60, 41359, 2394, 11508, 5529, 8977, 200, 152681, 152683, 604, 16996, 635, 40, 257, 957, 79594, 517, 10155

Offset: 1

Author

David James Sycamore, Feb 17 2016

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..5000 (first 2000 terms from Paolo P. Lava)

Crossrefs

Cf. A001414, A268868 (similar sequence with initial terms 1,1).

Programs

Mathematica

f[x_] := Total@ Flatten[ConstantArray[#1, #2] & @@@ FactorInteger[x]]; s = 3; {1, 2}~Join~Reap[Do[s += Sow@ f[s], {n, 3, 1000}] ][[-1, 1]] (* Michael De Vlieger, Jun 24 2025 *)

PARI

lista(nn) = {va = vector(nn); print1(va[1] = 1, ", "); print1(va[2] = 2, ", "); 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 19 2016