login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A284283 Let x be the sum of the divisors d_i of k such that d_i | sigma(k). Sequence lists the numbers k for which x^2 = sigma(k). 2
1, 66, 1092, 1416, 38280, 38760, 43080, 92960, 101024, 112672, 168210, 175230, 180090, 194130, 260400, 491536, 863772, 891996, 1004640, 1061400, 1234464, 1282848, 1294944, 2010528, 2041632, 2079648, 2090016, 3394440, 3653640, 3673080, 3701160, 5528250 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Subset of A006532.

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..111 (terms < 10^9)

EXAMPLE

Divisors of 66 are 1, 2, 3, 6, 11, 22, 33, 66 and sigma(66) = 144. Then:

144 / 1 = 144, 144 / 2 = 72, 144 /  3 = 48, 144 / 6 = 24 and (1 + 2 + 3 + 6)^2 = 12^2 = 144.

MAPLE

with(numtheory): P:=proc(q) local a, k, n, x;

for n from 1 to q do a:=sort([op(divisors(n))]); x:=0;

for k from 1 to nops(a)-1 do if type(sigma(n)/a[k], integer) then x:=x+a[k]; fi; od;

if x^2=sigma(n) then print(n); fi; od; end: P(10^9);

MATHEMATICA

Select[Range[10^5], (d = DivisorSigma[1, #]; IntegerQ@ Sqrt@ d && d == DivisorSigma[1, GCD[d, #]]^2) &] (* Giovanni Resta, Mar 28 2017 *)

CROSSREFS

Cf. A000203, A006532, A284284.

Sequence in context: A271757 A228996 A196789 * A168123 A240004 A231287

Adjacent sequences:  A284280 A284281 A284282 * A284284 A284285 A284286

KEYWORD

nonn

AUTHOR

Paolo P. Lava, Mar 24 2017

EXTENSIONS

a(1) and a(32) from Giovanni Resta, Mar 28 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 28 14:44 EDT 2022. Contains 357073 sequences. (Running on oeis4.)