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A291457 Numbers n having a proper divisor d such that sigma(n) - k*d = k*n. Case k = 3. 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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Case k=2 are the admirable numbers (A111592).
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
Sequence in context: A117551 A068545 A068403 * A329189 A364976 A289056
KEYWORD
nonn,easy
AUTHOR
Paolo P. Lava, Aug 24 2017
STATUS
approved

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)