A291457 Numbers n having a proper divisor d such that sigma(n) - k*d = k*n. Case k = 3.

180, 240, 360, 420, 480, 540, 600, 660, 780, 840, 1080, 1320, 1560, 1890, 1920, 2016, 2040, 2184, 2280, 2352, 2376, 2688, 2760, 2856, 3000, 3192, 3360, 3480, 3720, 3744, 4284, 4320, 4440, 4680, 4704, 4896, 4920, 5160, 5292, 5640, 5796, 6048, 6360, 6552, 7080, 7128

Offset

1,1

Comments

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

Subset of A023197, A068403, A068545, A204828, A204830.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1500 from Paolo P. Lava)

Example

One of the proper divisors of 1080 is 120 and sigma(1080) - 3*120 = 3600 - 360 = 3240 = 3*1080.
One of the proper divisors of 17850 is 6 and sigma(17850) - 3*6 = 53568 - 18 = 53550 = 3*17850.

Maple

with(numtheory): P:=proc(q, h) local a, b, c, k; c:=0; a:=sort([op(divisors(q))]); for k from 1 to nops(a)-1 do if sigma(q)-h*a[k]=h*q then c:=1; break; fi; od; if c=1 then q; fi; end: seq(P(i, 3), i=1..7200);

Mathematica

k=3; Select[Range[7128], (t = DivisorSigma[1, #]/k - #; # > t > 0 && IntegerQ[t] && Mod[#, t] == 0) &] (* Giovanni Resta, Aug 25 2017 *)

Crossrefs

Cf. A000203, A023197, A068403, A068545, A111592, A204828, A204830, A291458, A291459.

Sequence in context: A117551 A068545 A068403 * A329189 A364976 A289056

Adjacent sequences: A291454 A291455 A291456 * A291458 A291459 A291460

Keyword

nonn,easy

Author

Paolo P. Lava, Aug 24 2017

Status

approved