login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

RMS values of the RMS numbers: a(n) is the root mean square of the divisors of A140480(n).
7

%I #27 Oct 29 2019 07:53:10

%S 1,5,29,169,145,845,1105,2405,3445,4901,2665,5525,9425,12325,12025,

%T 17225,24505,13325,32045,55205,47125,61625,69745,101065,99905,77285,

%U 124501,160225,186745,204425,239425,160225,273325,276025,292825,226525,446165,456025

%N RMS values of the RMS numbers: a(n) is the root mean square of the divisors of A140480(n).

%C Those numbers seem to be congruent to 0,1,-1 mod 5. - _Ctibor O. Zizka_, Sep 23 2008

%C No, the first terms congruent to 2 and 3 mod 5 are a(461) = 247511537 and a(1603) = 7177834573, respectively. - _Giovanni Resta_, Oct 29 2019

%H Giovanni Resta, <a href="/A141812/b141812.txt">Table of n, a(n) for n = 1..7430</a> (terms 1..455 from Andrew Weimholt, terms 456..1660 from Donovan Johnson)

%e a(5)=145, because A140480(5)=287, with divisors 1,7,41,287 and RMS(1,7,41,287) = 145.

%t rmsQ[n_] := IntegerQ[Sqrt[DivisorSigma[2, n]/DivisorSigma[0, n]]]; Reap[ For[k=1; n=1, k<10^7, k++, If[rmsQ[k], an = Sqrt[Mean[Divisors[k]^2]]; Print["k = ", k, " a(", n++, ") = ", an]; Sow[an]]]][[2, 1]] (* _Jean-François Alcover_, Dec 04 2015 *)

%o (PARI) for(n=1,1e6,if(issquare(sumdiv(n,d,d^2)/numdiv(n),&s) && denominator(s)==1,print1(s", "))) \\ _Charles R Greathouse IV_, Mar 08 2013

%Y Cf. A140480, A141813, A141814, A141815, A141816.

%K nonn

%O 1,2

%A _Andrew Weimholt_, Jul 07 2008