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Integers that are exactly 2-deficient-perfect numbers.
2

%I #10 Jun 15 2021 01:30:20

%S 15,21,45,50,52,63,75,99,105,117,135,182,190,195,230,231,266,273,315,

%T 375,405,435,495,585,592,656,688,850,891,950,1155,1215,1305,1365,1395,

%U 1612,1755,1845,1862,1875,1892,1989,2079,2295,2312,2332,2336,2350,2366,2475

%N Integers that are exactly 2-deficient-perfect numbers.

%H FengJuan Chen, <a href="http://math.colgate.edu/~integers/t37/t37.Abstract.html">On Exactly k-deficient-perfect Numbers</a>, Integers, 19 (2019), Article A37, 1-9.

%e 117 is an exactly 2-deficient-perfect number with d1=13 and d2=39: sigma(117) = 182 = 2*117 - (13 + 39). See Theorem 1 p. 2 of FengJuan Chen.

%t def2[n_] := Catch@Block[{s = 2*n - DivisorSigma[1, n], d}, If[s > 0, d = Most@ Divisors@ n; Do[If[s == d[[i]] + d[[j]], Throw@ True], {i, 2, Length@ d}, {j, i-1}]; False]]; Select[Range[2500], def2] (* _Giovanni Resta_, Jan 23 2020 *)

%Y Cf. A000203 (sigma), A271816 (deficient-perfect numbers (k=1)), A331627 (k-deficient-perfect), A331629 (3-deficient-perfect).

%K nonn

%O 1,1

%A _Michel Marcus_, Jan 23 2020

%E More terms from _Giovanni Resta_, Jan 23 2020