A020486 Average of squares of divisors is an integer: numbers k such that sigma_0(k) divides sigma_2(k).

1, 3, 4, 5, 7, 11, 12, 13, 15, 17, 19, 20, 21, 23, 25, 27, 28, 29, 31, 33, 35, 37, 39, 41, 43, 44, 47, 48, 49, 51, 52, 53, 55, 57, 59, 60, 61, 65, 67, 68, 69, 71, 73, 75, 76, 77, 79, 83, 84, 85, 87, 89, 91, 92, 93, 95, 97, 100, 101, 103, 105, 107, 108, 109, 111, 112, 113, 115, 116

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

If sigma_2(k)/sigma_0(k) is a square then k is an RMS-number (A140480). - Ctibor O. Zizka, Jul 14 2008

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)

Crossrefs

Cf. A000005, A001157, A140480.

Programs

Haskell

a020486 n = a020486_list !! (n-1)
a020486_list = filter (\x -> a001157 x `mod` a000005 x == 0) [1..]
-- Reinhard Zumkeller, Jan 15 2013

Magma

[n: n in [1..120] | IsZero(DivisorSigma(2, n) mod NumberOfDivisors(n))]; // Bruno Berselli, Apr 11 2013

Mathematica

Select[Range[150],Divisible[DivisorSigma[2,#],DivisorSigma[0,#]]&] (* Harvey P. Dale, May 03 2011 *)

PARI

is(n)=sigma(n,2)%numdiv(n)==0 \\ Charles R Greathouse IV, Jul 02 2013

Formula

A001157(k) mod A000005(k) = 0. - Reinhard Zumkeller, Jan 15 2013