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%I #28 Apr 03 2023 10:36:13
%S 1,9,25,37,63,71876888199
%N Numbers k such that Sum_{i=1..k} sigma(i) is divisible by Sum_{i=1..k} d(i), where sigma(i) = sum of divisors of i (A000203), and d(i) = number of divisors of i (A000005).
%C No other terms below 2^36. - _Alex Ratushnyak_, Jun 29 2013
%C The ratio corresponding to a(6) is 4249100789716352394810 / 1807894350282 = 2350303705. a(7) > 10^12. - _Giovanni Resta_, Apr 13 2017
%H C. K. Caldwell, and G. L. Honaker, Jr., <a href="https://t5k.org/curios/page.php?curio_id=29587">Prime curio for 37</a>
%F Numbers k such that A006218(k) divides A024916(k).
%e A006218(9) = 23, A024916(9) = 69, 23 divides 69, so 9 is in the sequence.
%t Flatten[Position[Accumulate[Table[{DivisorSigma[1,n],DivisorSigma[0,n]},{n,100}]],_?(Divisible[First[#],Last[#]]&),{1},Heads->False]] (* _Harvey P. Dale_, Jun 19 2013 *)
%o (PARI) isok(n) = sum(k=1, n, sigma(k)) % sum(k=1, n, numdiv(k)) == 0; \\ _Michel Marcus_, Jul 07 2016
%Y Cf. A000005, A000203, A006218, A024916.
%K nonn,more
%O 1,2
%A _Alex Ratushnyak_, Jun 13 2013
%E a(6) from _Giovanni Resta_, Apr 12 2017
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