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

1,2

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

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A015537 A182017 A291017 * A227206 A001653 A141814

Adjacent sequences: A141809 A141810 A141811 * A141813 A141814 A141815

Keyword

nonn

Author

Andrew Weimholt, Jul 07 2008

Status

approved