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A218464 Numbers n = (sum_(j=1...k) tau(j)) with n divisible by k, where tau(j) is the number of divisors of j. 1
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 (list; graph; refs; listen; history; text; internal format)
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

Number a(3) = 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

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Last modified October 20 07:23 EDT 2019. Contains 328252 sequences. (Running on oeis4.)