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URL: https://oeis.org/A331629

⇱ A331629 - OEIS

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A331629
Integers that are exactly 3-deficient-perfect numbers.
4
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.
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
LINKS
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
KEYWORD
nonn
AUTHOR
Michel Marcus, Jan 23 2020
EXTENSIONS
More terms from Giovanni Resta, Jan 23 2020
STATUS
approved