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

1,2

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)

Formula

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A087086 A301587 A319796 * A125225 A092903 A005153

Adjacent sequences: A103285 A103286 A103287 * A103289 A103290 A103291

Keyword

nonn

Author

Max Alekseyev, Jan 28 2005

Status

approved