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

Author

Paolo P. Lava, Mar 26 2013

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A000005, A168133.

Cf. A050226 (has the values of k).

Programs

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 *)

Extensions

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