A091290 Numbers k such that sigma(k) + sigma(k+1) <= sigma(2*k+1).

1, 4, 7, 10, 13, 22, 31, 37, 46, 49, 52, 58, 61, 67, 73, 82, 85, 94, 97, 106, 112, 115, 121, 127, 130, 136, 142, 148, 157, 166, 172, 178, 181, 187, 193, 202, 211, 214, 217, 226, 229, 232, 238, 241, 247, 253, 256, 262, 274, 277, 283, 292, 298, 301, 307, 310, 313

Offset

1,2

Comments

The numbers of terms that do not exceed 10^k, for k = 1, 2, ..., are 4, 19, 173, 1837, 18241, 182810, 1829411, 18292269, 182909074, 1829124992, ... . Apparently, the asymptotic density of this sequence exists and equals 0.18291... . - Amiram Eldar, Feb 11 2025

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Mathematica

Do[s=(DivisorSigma[1, n]+DivisorSigma[1, n+1])/ DivisorSigma[1, 2*n+1]; If[ !Greater[s, 1], Print[n]], {n, 1, 10000000}]

Prog

(PARI) is(n)=sigma(n)+sigma(n+1)<=sigma(2*n+1) \\ Charles R Greathouse IV, Feb 14 2013

Crossrefs

Cf. A000203 (sigma), A067171, A091287, A091289.

Sequence in context: A002640 A096675 A069212 * A119256 A143454 A318774

Adjacent sequences: A091287 A091288 A091289 * A091291 A091292 A091293

Keyword

nonn

Author

Labos Elemer, Feb 16 2004

Extensions

New name from Charles R Greathouse IV, Feb 14 2013

Status

approved