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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
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. A050226 (has the values of k).
Sequence in context: A240036 A091632 A060768 * A060809 A112547 A015657
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Mar 26 2013
EXTENSIONS
a(22)-a(30) from Giovanni Resta, Mar 28 2013
STATUS
approved