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).

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

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