login
A190122
a(n) = Sum_{k=1..n} k*lcm(k,k')/gcd(k,k'), where k' is arithmetic derivative of k.
1
0, 4, 13, 17, 42, 222, 271, 319, 373, 1073, 1194, 1338, 1507, 3271, 5071, 5103, 5392, 6148, 6509, 7109, 11519, 17811, 18340, 19924, 20174, 30314, 30341, 31909, 32750, 60650, 61611, 61931, 77177, 99141, 113841, 114381, 115750, 146074, 170410, 177210, 178891
OFFSET
1,2
COMMENTS
Use lcm(1,0)=0 and gcd(1,0)=1.
LINKS
FORMULA
a(n) = Sum_{k=1..n} k*A189036(k).
EXAMPLE
lcm(1,1')/gcd(1,1')*1+lcm(2,2')/gcd(2,2')*2+lcm(3,3')/gcd(3,3')*3=0+2/1*2+3/1*3=13 ->a(3)=13.
MAPLE
der:=n->n*add(op(2, p)/op(1, p), p=ifactors(n)[2]):
seq(add(lcm(der(i), i)/gcd(der(i), i)*i, i=1..n), n=1..50);
MATHEMATICA
A003415[n_]:= If[Abs@n < 2, 0, n Total[#2/#1 & @@@FactorInteger[Abs@n]]];
Table[Sum[k*LCM[k, A003415[k]]/GCD[k, A003415[k]], {k, 1, n}], {n, 1, 50}] (* G. C. Greubel, Dec 29 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Giorgio Balzarotti, May 04 2011
STATUS
approved