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A020486 Average of squares of divisors is an integer: sigma_0(n) divides sigma_2(n). 14
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

FORMULA

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

MAPLE

with(numtheory); List020486:=proc(q) local a, b, k, n;

for n from 1 to q do a:=divisors(n); b:=add(a[k]^2, k=1..nops(a));

if type(b/tau(n), integer) then print(n); fi; od; end:

List020486(10^6); # Paolo P. Lava, Apr 11 2013

MATHEMATICA

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

PROG

(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

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

CROSSREFS

Cf. A140480.

Sequence in context: A088130 A046840 A057773 * A091428 A047499 A330109

Adjacent sequences: A020483 A020484 A020485 * A020487 A020488 A020489

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified December 3 08:35 EST 2022. Contains 358515 sequences. (Running on oeis4.)