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

1,1

Comments

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

Links

Table of n, a(n) for n=1..46.

Saralee Aursukaree and Prapanpong Pongsriiam, On Exactly 3-Deficient-Perfect Numbers, arXiv:2001.06953 [math.NT], 2020.

Example

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

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 *)

Crossrefs

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

Sequence in context: A294311 A252369 A252362 * A248943 A248649 A050238

Adjacent sequences: A331626 A331627 A331628 * A331630 A331631 A331632

Keyword

nonn

Author

Michel Marcus, Jan 23 2020

Extensions

More terms from Giovanni Resta, Jan 23 2020

Status

approved