A141800 For n >= 2, a(n) = Sum_{k=1..n} (smallest prime dividing (n*k)). a(1)=0.

0, 4, 8, 8, 17, 12, 28, 16, 23, 20, 50, 24, 67, 28, 38, 32, 95, 36, 118, 40, 53, 44, 152, 48, 81, 52, 68, 56, 201, 60, 236, 64, 83, 68, 112, 72, 293, 76, 98, 80, 345, 84, 392, 88, 113, 92, 450, 96, 185, 100, 128, 104, 525, 108, 176, 112, 143, 116, 604, 120, 669, 124, 158

Offset

1,2

Links

Diana Mecum, Table of n, a(n) for n = 1..1000

Example

For n = 5, the smallest prime dividing 1*5=5 is 5. The smallest prime dividing 2*5=10 is 2. The smallest prime dividing 3*5=15 is 3. The smallest prime dividing 4*5=20 is 2. And the smallest prime dividing 5*5=25 is 5. So a(5) = 5+2+3+2+5 = 17.

Mathematica

Table[sum=0; Do[sum=sum+Min[Divisors[k*n][[2]], Divisors[n][[2]]], {k, 1, n}];
sum, {n, 2, 1000}]; (* then manually add in a(0) term *) (* Diana L. Mecum, Jan 02 2009 *)

Crossrefs

Cf. A141801.

Sequence in context: A209382 A298119 A089474 * A019197 A066106 A030296

Adjacent sequences: A141797 A141798 A141799 * A141801 A141802 A141803

Keyword

nonn

Author

Leroy Quet, Jul 05 2008

Extensions

a(10)-a(63) from Diana L. Mecum, Jan 02 2009

Status

approved