A331629 Integers that are exactly 3-deficient-perfect numbers.

130, 154, 170, 182, 232, 250, 290, 434, 484, 848, 944, 950, 988, 1196, 1210, 1274, 1276, 1450, 1521, 1564, 1666, 1892, 1924, 2618, 2848, 2888, 2926, 3094, 3232, 3424, 3458, 3542, 3616, 4186, 4214, 4250, 4522, 4750, 4810, 5150, 5278, 5330, 5510, 5590, 5642, 5890

Offset: 1

Author

Michel Marcus, Jan 23 2020

Keywords

• nonn

Comments

Aursukaree & Pongsriiam prove that 1521 is the only odd term with at most two distinct prime factors.

Numbers k that have 3 distinct proper divisors, d_1, d_2 and d_3, such that sigma(k) = 2*k - (d_1 + d_2 + d_3). - Amiram Eldar, Dec 29 2024

Examples

			130 is an exactly 3-deficient-perfect number with d1=1, d2=2 and d3=5: sigma(130) = 252 = 2*130 - (1+2+5).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000
• Saralee Aursukaree and Prapanpong Pongsriiam, On Exactly 3-Deficient-Perfect Numbers, arXiv:2001.06953 [math.NT], 2020.

Crossrefs

Cf. A000203 (sigma), A271816 (deficient-perfect numbers (k=1)), A331627 (k-deficient-perfect), A331628 (2-deficient-perfect).

Programs

Mathematica

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 *)

Extensions

More terms from Giovanni Resta, Jan 23 2020