A291485 Numbers m such that sigma(x) = m*(m+1)/2 has at least one solution.
1, 2, 3, 5, 7, 8, 12, 13, 15, 18, 20, 24, 27, 30, 31, 32, 35, 38, 39, 47, 48, 51, 55, 56, 62, 63, 64, 79, 80, 84, 90, 92, 95, 96, 104, 111, 116, 119, 120, 128, 135, 140, 142, 143, 144, 147, 152, 155, 156, 159, 160, 167, 168, 170, 171, 175, 176, 182, 184, 188, 191, 192, 195, 203, 207, 208
Offset: 1
Examples
15 is a term because sigma(54) = sigma(56) = sigma(87) = sigma(95) = A000217(15).
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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Maple
N:= 1000: # to get all terms <= N Sigmas:= {seq(numtheory:-sigma(x),x=1..N*(N+1)/2)}: select(t -> member(t*(t+1)/2, Sigmas), [$1..N]); # Robert Israel, Aug 25 2017
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Mathematica
invT[n_] := (Sqrt[8*n+1]-1)/2; Union@ Select[invT /@ DivisorSigma[1, Range[ 208*209/2]], IntegerQ[#] && # <= 208 &] (* Giovanni Resta, Aug 25 2017 *)
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