A190118 a(n) = Sum_{k=1..n} k/gcd(k,k'), where n' is arithmetic derivative of n.

1, 3, 6, 7, 12, 18, 25, 27, 30, 40, 51, 54, 67, 81, 96, 97, 114, 120, 139, 144, 165, 187, 210, 216, 221, 247, 248, 255, 284, 314, 345, 347, 380, 414, 449, 452, 489, 527, 566, 576, 617, 659, 702, 713, 728, 774, 821, 824, 831, 841

Offset

1,2

Comments

Use gcd(1,0)=1.

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Example

1/gcd(1,1')+2/gcd(2,2')+3/gcd(3,3')=1+2/1+3/1=6 ->a(3)=6.

Maple

der:=n->n*add(op(2, p)/op(1, p), p=ifactors(n)[2]):
seq(add(i/gcd(der(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/GCD[k, A003415[k]], {k, 1, n}], {n, 1, 50}] (* G. C. Greubel, Dec 29 2017 *)

Crossrefs

Cf. A003415.

Sequence in context: A332904 A370900 A069891 * A249714 A250177 A333002

Adjacent sequences: A190115 A190116 A190117 * A190119 A190120 A190121

Keyword

nonn

Author

Giorgio Balzarotti, May 04 2011

Status

approved