A063449 Numbers k for which d(k+1) > 2*d(k), where d(j) = A000005(j).

11, 17, 19, 23, 29, 31, 35, 41, 43, 47, 53, 59, 67, 71, 79, 83, 89, 95, 97, 101, 103, 107, 109, 111, 113, 119, 125, 127, 131, 137, 139, 143, 149, 151, 155, 159, 161, 163, 167, 169, 173, 179, 181, 191, 197, 199, 203, 209, 211, 215, 219, 223, 227, 229, 233, 239

Offset

1,1

Comments

d(p+1) >= 2d(p) holds for all primes p and for some composite integers, as well.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harry J. Smith)

Example

For k = 29: 2*d(29) = 2*2 = 4 < 8 = d(30).
For k = 95: 2*d(95) = 2*4 = 8 < 12 = d(96).

Mathematica

Position[Partition[DivisorSigma[0, Range[250]], 2, 1], _?(2#[[1]]<#[[2]]&), 1, Heads->False]//Flatten (* Harvey P. Dale, Nov 16 2020 *)

Prog

(PARI) is(m) = numdiv(m + 1) > 2*numdiv(m); \\ Harry J. Smith, Aug 21 2009

Crossrefs

Cf. A000005, A063446, A063450.

Sequence in context: A050891 A226630 A061751 * A157996 A050713 A217063

Adjacent sequences: A063446 A063447 A063448 * A063450 A063451 A063452

Keyword

nonn,changed

Author

Labos Elemer, Jul 24 2001

Extensions

Edited by Jon E. Schoenfield, Sep 05 2017

Status

approved