A088823 a(n) is the GCD of the sum of largest prime factors of numbers from 1 to n and of the sum of smallest prime factors of numbers from 1 to n.

0, 2, 5, 7, 12, 1, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 6, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 3, 4, 1, 3, 1, 2, 3, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 10, 1, 1, 1, 2, 29, 1, 1, 2, 1, 7, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 2, 1, 5, 1, 14, 1, 1

Offset: 1

Author

Labos Elemer, Oct 22 2003

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A088821, A088822, A088824, A088825.

Programs

Maple

map(igcd@op, ListTools:-PartialSums([[0,0],seq([min,max](numtheory:-factorset(n)),n=2..N)])); # Robert Israel, Dec 16 2015

Mathematica

GCD @@@ Transpose[{Accumulate[Prepend[First /@ #, 0]], Accumulate[Prepend[Last /@ #, 0]]}] &@ Map[First /@ FactorInteger@ # &, Range[2, 103]] (* Michael De Vlieger, Dec 15 2015 *)

Formula

a(n) = gcd(A088821(n), A088822(n)).