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%I #14 Jun 15 2021 01:38:36
%S 130,154,170,182,232,250,290,434,484,848,944,950,988,1196,1210,1274,
%T 1276,1450,1521,1564,1666,1892,1924,2618,2848,2888,2926,3094,3232,
%U 3424,3458,3542,3616,4186,4214,4250,4522,4750,4810,5150,5278,5330,5510,5590,5642,5890
%N Integers that are exactly 3-deficient-perfect numbers.
%C Aursukaree & Pongsriiam prove that 1521 is the only odd term with at most two distinct prime factors.
%H Saralee Aursukaree and Prapanpong Pongsriiam, <a href="https://arxiv.org/abs/2001.06953">On Exactly 3-Deficient-Perfect Numbers</a>, arXiv:2001.06953 [math.NT], 2020.
%e 130 is an exactly 3-deficient-perfect number with d1=1, d2=2 and d3=5: sigma(130) = 252 = 2*130 - (1+2+5).
%t def3[n_] := Catch@ Block[{s = 2*n - DivisorSigma[1, n], d}, If[s > 0, d = Most@ Divisors@ n; Do[If[s == d[[i]] + d[[j]] + d[[k]], Throw@ True], {i, 3, Length@ d}, {j, i-1}, {k, j-1}]; False]]; Select[ Range[6000], def3] (* _Giovanni Resta_, Jan 23 2020 *)
%Y Cf. A000203 (sigma), A271816 (deficient-perfect numbers (k=1)), A331627 (k-deficient-perfect), A331628 (2-deficient-perfect).
%K nonn
%O 1,1
%A _Michel Marcus_, Jan 23 2020
%E More terms from _Giovanni Resta_, Jan 23 2020
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