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Numbers n such that the average of all proper divisors of all positive integers <= n is an integer.
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%I #6 Apr 13 2017 04:05:53

%S 2,3,63,1249,4696,1200509

%N Numbers n such that the average of all proper divisors of all positive integers <= n is an integer.

%C Numbers n such that A002541(n)|A153485(n).

%C a(7) > 10^12. - _Giovanni Resta_, Apr 13 2017

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RestrictedDivisorFunction.html">Restricted Divisor Function</a>

%H <a href="/index/Su#sums_of_divisors">Index entries for sequences related to sums of divisors</a>

%t Select[Range[2, 1300000], Mod[Sum[DivisorSigma[1, k] - k, {k, 1, #}], Sum[DivisorSigma[0, k] - 1, {k, 1, #}]] == 0 &]

%Y Cf. A000005, A000203, A001065, A002541, A003601, A023884, A023886, A027751, A153485, A226647, A284288.

%K nonn,more

%O 1,1

%A _Ilya Gutkovskiy_, Apr 02 2017