A331628 Integers that are exactly 2-deficient-perfect numbers.

15, 21, 45, 50, 52, 63, 75, 99, 105, 117, 135, 182, 190, 195, 230, 231, 266, 273, 315, 375, 405, 435, 495, 585, 592, 656, 688, 850, 891, 950, 1155, 1215, 1305, 1365, 1395, 1612, 1755, 1845, 1862, 1875, 1892, 1989, 2079, 2295, 2312, 2332, 2336, 2350, 2366, 2475

Offset: 1

Author

Michel Marcus, Jan 23 2020

Keywords

• nonn

Comments

Numbers k that have 2 distinct proper divisors, d_1 and d_2, such that sigma(k) = 2*k - (d_1 + d_2). - Amiram Eldar, Dec 29 2024

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000
• FengJuan Chen, On Exactly k-deficient-perfect Numbers, Integers, 19 (2019), Article A37, 1-9.

Crossrefs

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

Programs

Mathematica

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 *)

Extensions

More terms from Giovanni Resta, Jan 23 2020