A103288 Numbers k such that sigma(k) >= 2k-1 (union of perfect, abundant and least deficient numbers).

1, 2, 4, 6, 8, 12, 16, 18, 20, 24, 28, 30, 32, 36, 40, 42, 48, 54, 56, 60, 64, 66, 70, 72, 78, 80, 84, 88, 90, 96, 100, 102, 104, 108, 112, 114, 120, 126, 128, 132, 138, 140, 144, 150, 156, 160, 162, 168, 174, 176, 180, 186, 192, 196, 198, 200, 204, 208, 210, 216, 220

Offset: 1

Author

Max Alekseyev, Jan 28 2005

Keywords

• nonn

Comments

If the only least deficient numbers are the powers of 2 (open problem) then this sequence is the union of A023196 and A000079.

Like the abundant numbers, this sequence has density between 0.2474 and 0.2480, see A005101. - Charles R Greathouse IV, Nov 30 2022

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)

Crossrefs

Cf. A023196, A023197, A023198, A023199, A000079, A004125.

Programs

Mathematica

Select[Range[500], DivisorSigma[1, #] >= 2*# - 1 &] (* Paolo Xausa, Dec 09 2024 *)

PARI

for(n=1,1000,if(sigma(n)>=2*n-1,print(n)));

Formula

Numbers k such that A004125(k) <= A004125(k-1).