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

1,1

Links

Table of n, a(n) for n=1..50.

FengJuan Chen, On Exactly k-deficient-perfect Numbers, Integers, 19 (2019), Article A37, 1-9.

Example

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.

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 *)

Crossrefs

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

Sequence in context: A063175 A367103 A325658 * A171569 A247021 A334117

Adjacent sequences: A331625 A331626 A331627 * A331629 A331630 A331631

Keyword

nonn

Author

Michel Marcus, Jan 23 2020

Extensions

More terms from Giovanni Resta, Jan 23 2020

Status

approved