A141812 RMS values of the RMS numbers: a(n) is the root mean square of the divisors of A140480(n).

1, 5, 29, 169, 145, 845, 1105, 2405, 3445, 4901, 2665, 5525, 9425, 12325, 12025, 17225, 24505, 13325, 32045, 55205, 47125, 61625, 69745, 101065, 99905, 77285, 124501, 160225, 186745, 204425, 239425, 160225, 273325, 276025, 292825, 226525, 446165, 456025

Offset: 1

Author

Andrew Weimholt, Jul 07 2008

Keywords

• nonn

Comments

Those numbers seem to be congruent to 0,1,-1 mod 5. - Ctibor O. Zizka, Sep 23 2008

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

Examples

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

Links

• Giovanni Resta, Table of n, a(n) for n = 1..7430 (terms 1..455 from Andrew Weimholt, terms 456..1660 from Donovan Johnson)

Crossrefs

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

Programs

Mathematica

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 *)

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