A133133 a(n) is the largest prime factor of the sum of the largest prime factors of numbers from 2 to n.

2, 5, 7, 3, 5, 11, 3, 3, 2, 43, 23, 59, 11, 71, 73, 5, 31, 7, 13, 31, 5, 79, 23, 83, 179, 13, 7, 109, 223, 127, 2, 89, 71, 97, 7, 331, 7, 11, 23, 409, 13, 17, 47, 19, 83, 109, 137, 37, 7, 577, 59, 643, 19, 73, 83, 683, 89, 257, 97, 31, 31, 7, 877, 89, 53, 11, 197, 7, 29, 181, 11

Offset: 2

Author

Paul Finley (pfinley(AT)touro.edu), Sep 21 2007

Keywords

• easy
• nonn
• look

Examples

			a(11) = gpf(43) = 43;
a(12) = gpf(46) = 23.
		

Links

• Robert Israel, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A006530, A088822.

Programs

Maple

gpf:= proc(n) max(numtheory:-factorset(n)) end proc:
map(gpf, ListTools:-PartialSums(map(gpf, [$2..100])));

Mathematica

FactorInteger[#][[-1,1]]&/@Accumulate[Table[FactorInteger[n][[-1,1]],{n,2,80}]] (* Harvey P. Dale, Feb 01 2025 *)

PARI

gpf(n) = vecmax(factor(n)[,1]);
a(n) = gpf(sum(k=2, n, gpf(k))); \\ Michel Marcus, Jun 02 2021