A271441 a(1) = 2; if gpf(a(n-1)) <= n-1 then a(n) = a(n-1) + a(gpf(a(n-1))), else a(n) = a(n-1) + 1, where gpf(m) is the greatest prime factor of m.

2, 3, 4, 7, 8, 11, 12, 16, 19, 20, 28, 40, 48, 52, 100, 108, 112, 124, 125, 133, 258, 259, 260, 308, 336, 348, 349, 350, 362, 363, 391, 651, 1042, 1043, 1044, 1406, 1407, 1408, 1436, 1437, 1438, 1439, 1440, 1448, 1449, 1709, 1710, 1835, 1836, 1948

Offset

1,1

Comments

Choosing the initial value a(1) = 2 seems to produce the most irregular sequence.

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Example

Since a(11) = 28, gpf(28) = 7 and a(7) = 12, then a(12) = 28 + 12 = 40.

Mathematica

Nest[Append[#, (x = #[[-1]]) + If[(p = FactorInteger[x][[-1, 1]]) <= Length@#, #[[p]], 1]] &, {2}, 49] (* Ivan Neretin, Jan 27 2017 *)

Prog

(PARI) gpf(n) = if (n==1, 1, vecmax(factor(n)[, 1]));
lista(nn) = {va = vector(nn); print1(va[1] = 2, ", "); for (n=2, nn, if (gpf(va[n-1]) <= n-1, va[n] = va[n-1] + va[gpf(va[n-1])], va[n] = va[n-1]+1); print1(va[n], ", "); ); } \\ Michel Marcus, Apr 09 2016

Crossrefs

Cf. A006530 (gpf).

Sequence in context: A342028 A368402 A284937 * A328421 A003508 A225229

Adjacent sequences: A271438 A271439 A271440 * A271442 A271443 A271444

Keyword

nonn,hear

Author

Cody M. Haderlie, Apr 07 2016

Status

approved