A218464 Numbers m = (Sum_(j=1..k) tau(j)) with m divisible by k, where tau(j) is the number of divisors of j.

1, 8, 10, 45, 168, 176, 188, 605, 2016, 2040, 2082, 6510, 20384, 62433, 62523, 564542, 4928261, 4928703, 4928729, 42018075, 351871865, 1012753620, 1012755546, 2905896480, 2905898228, 192057921660, 1542529159875, 12309661243665, 12309661255437, 34700429419432

Offset

1,2

Comments

See A050226 for the values of k. - T. D. Noe, Mar 27 2013

Links

Giovanni Resta, Table of n, a(n) for n = 1..39 (based on A050226 values)

Example

10 is in sequence because k=5 divides the sum of tau(1) + tau(2) + tau(3) + tau(4) + tau(5) = 1+2+2+3+2 = 10.

Maple

with(numtheory);
A218464:=proc(q)  local n;  a:=0;
for n from 1 to q do a:=a+tau(n) if type(a/n, integer) then print(a); fi; od; end:
A218464 (10^10); # Paolo P. Lava, Mar 26 2013

Mathematica

sm = 0; t = {}; Do[sm = sm + DivisorSigma[0, n]; If[Mod[sm, n] == 0, AppendTo[t, sm]], {n, 1000}]; t (* T. D. Noe, Mar 27 2013 *)

Crossrefs

Cf. A000005, A168133.

Cf. A050226 (has the values of k).

Sequence in context: A240036 A091632 A060768 * A060809 A112547 A015657

Adjacent sequences: A218461 A218462 A218463 * A218465 A218466 A218467

Keyword

nonn

Author

Paolo P. Lava, Mar 26 2013

Extensions

a(22)-a(30) from Giovanni Resta, Mar 28 2013

Status

approved