cp's OEIS Frontend

A279814 Numbers n such that the average of the squares of the proper divisors of n is an integer.

%I A279814 #10 Jul 26 2019 17:00:57
%S A279814 2,3,5,7,8,9,10,11,13,14,17,19,22,23,25,26,29,31,34,35,37,38,41,43,46,
%T A279814 47,49,50,53,55,58,59,61,62,65,67,71,73,74,75,77,79,80,81,82,83,85,86,
%U A279814 89,91,94,95,97,101,103,106,107,109,113,115,118,119,121,122,125,127,131,133,134,137,139,140,142,143,145,146,149
%N A279814 Numbers n such that the average of the squares of the proper divisors of n is an integer.
%C A279814 Numbers n such that number of proper divisors of n (A032741) divides sum of squares of proper divisors of n (A067558).
%C A279814 All the prime numbers are in this sequence.
%H A279814 Charles R Greathouse IV, <a href="/A279814/b279814.txt">Table of n, a(n) for n = 1..10000</a>
%H A279814 <a href="/index/Su#sums_of_divisors">Index entries for sequences related to sums of divisors</a>
%e A279814 8 is in the sequence because 8 has 3 proper divisors {1,2,4}, 1^2 + 2^2 + 4^2 = 21 and 3 divides 21.
%t A279814 Select[Range[150], Mod[DivisorSigma[2, #1] - #1^2, DivisorSigma[0, #1] - 1] == 0 &]
%t A279814 Select[Range[200],IntegerQ[Mean[Most[Divisors[#]]^2]]&] (* _Harvey P. Dale_, Jul 26 2019 *)
%o A279814 (PARI) is(n)=my(d=divisors(n)); d=apply(k->k^2, d[1..#d-1]); n>1 && sum(i=1,#d,d[i])%#d==0 \\ _Charles R Greathouse IV_, Dec 19 2016
%Y A279814 Cf. A020486, A023884, A032741, A067558.
%K A279814 nonn,easy
%O A279814 1,1
%A A279814 _Ilya Gutkovskiy_, Dec 19 2016