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%I #11 Sep 23 2022 13:15:06
%S 287,1673,3055,6665,9545,9799,9855,21385,26095,34697,46655,66815,
%T 68593,68985,125255,155287,182665,242879,273265,380511,391345,404055,
%U 421655,627215,730145,814463,823537,876785,1069895,1087009,1166399,1204281,1256489,1289441
%N Composite RMS numbers: composite numbers c such that root mean square of divisors of c is an integer.
%C a(n) = composite number c (A002808), iff sqrt(sigma_2(c)/tau(c) = sqrt(A001157(c)/A000005(c)= k, for k = natural numbers (A000027). Prime RMS numbers (NSW primes) in A088165.
%C 16 of the first 1654 terms are even (the smallest is 2217231104). The first 16 even terms are all divisible by 30976. - _Donovan Johnson_, Apr 17 2013
%H Giovanni Resta, <a href="/A158287/b158287.txt">Table of n, a(n) for n = 1..7424</a> (terms < 10^13, first 1654 terms from Donovan Johnson)
%e a(1) = 287, sqrt(A001157(287)/A000005(287)) = sqrt(84100/4) = 145, number 145 is integer.
%t Select[Range[13*10^5],CompositeQ[#]&&IntegerQ[RootMeanSquare[Divisors[ #]]]&] (* _Harvey P. Dale_, Sep 23 2022 *)
%Y Cf. A001157, A000005, A088165, A140480.
%K nonn
%O 1,1
%A _Jaroslav Krizek_, Mar 15 2009
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