A291458 Numbers n having a proper divisor d such that sigma(n) - k*d = k*n. Case k = 4.

27720, 60480, 65520, 90720, 98280, 105840, 115920, 120120, 120960, 128520, 131040, 143640, 151200, 163800, 180180, 191520, 205920, 207900, 211680, 218400, 229320, 235620, 241920, 249480, 264600, 272160, 289800, 292320, 312480, 332640, 360360, 372960, 393120, 414960

Offset

1,1

Comments

Case k=2 are the admirable numbers (A111592).

Subset of A023198, A068404, A204831, A230608.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

One of the proper divisors of 27720 is 360 and sigma(27720) - 4*360 = 112320 - 1440 = 110880 = 4*27720.
One of the proper divisors of 115920 is 144 and sigma(115920) - 4*144 = 464256 - 576 = 463680 = 4*115920.

Maple

with(numtheory): P:=proc(q, h) local a, k, n; for n from 1 to q do a:=sort([op(divisors(n))]);
for k from 1 to nops(a)-1 do if sigma(n)-h*a[k]=h*n then print(n); break; fi; od; od; end: P(10^9, 4);

Mathematica

With[{k = 4}, Select[Range[5 * 10^5], Function[n, AnyTrue[Most@ Divisors@ n, DivisorSigma[1, n] - k # == k n &]]]] (* Michael De Vlieger, Aug 24 2017 *)
(* or *)
k=4; Select[Range[5*^5], (t = DivisorSigma[1, #]/k - #; #>t>0 && IntegerQ[t] && Mod[#, t] == 0) &] (* much faster, Giovanni Resta, Aug 25 2017 *)

Crossrefs

Cf. A000203, A023198, A068404, A111592, A204831, A230608, A291457, A291459.

Sequence in context: A068404 A279091 A307114 * A023943 A210161 A358414

Adjacent sequences: A291455 A291456 A291457 * A291459 A291460 A291461

Keyword

nonn,easy

Author

Paolo P. Lava, Aug 24 2017

Status

approved