A141801 For n>=2, a(n) = Sum_{k=1..n} (largest prime dividing (n*k)), a(1)=0.

0, 4, 9, 9, 25, 20, 49, 26, 33, 52, 121, 52, 169, 108, 93, 75, 289, 100, 361, 144, 179, 258, 529, 168, 195, 358, 189, 254, 841, 254, 961, 258, 431, 612, 363, 302, 1369, 766, 595, 404, 1681, 494, 1849, 656, 511, 1124, 2209, 556, 639, 598, 1009, 870, 2809, 654, 875

Offset

1,2

Comments

If n is prime, a(n) = n^2. - Robert Israel, Nov 07 2019

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

For n = 4, the largest prime dividing 1*4=4 is 2. The largest prime dividing 2*4=8 is 2. The largest prime dividing 3*4=12 is 3. And the largest prime dividing 4*4=16 is 2. So a(4) = 2+2+3+2 = 9.

Maple

lpf:= proc(n) option remember; max(numtheory:-factorset(n)) end proc:
f:= proc(n) local k; add(max(lpf(k), lpf(n)), k=1..n) end proc;
f(1):= 0:
map(f, [$1..100]); # Robert Israel, Nov 07 2019

Mathematica

lpf[n_] := lpf[n] = Max[FactorInteger[n][[All, 1]]];
a[n_] := Sum[Max[lpf[k], lpf[n]], {k, 1, n}];
a[1] = 0;
Array[a, 100] (* Jean-François Alcover, Jul 23 2020, after Maple *)

Crossrefs

Cf. A141800.

Sequence in context: A329732 A298816 A095873 * A177083 A081949 A091657

Adjacent sequences: A141798 A141799 A141800 * A141802 A141803 A141804

Keyword

nonn,look

Author

Leroy Quet, Jul 05 2008

Extensions

Extended by Ray Chandler, Jun 22 2009

Status

approved