A063450 - OEIS

A063450

Numbers k such that d(k+1) < 2*d(k), where d() is the number of divisors function A000005.

2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 36, 38, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 56, 57, 58, 60, 62, 63, 64, 66, 68, 70, 72, 74, 75, 76, 78, 80, 81, 82, 84, 85, 86, 88, 90, 91, 92, 93, 94, 96, 98, 99, 100, 102, 104, 105

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

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

EXAMPLE

d(k+1) < 2*d(k) holds mainly for composites and for the primes 2 and 3. E.g.:

For k = 10: 2*d(10) = 2*4 = 8 > 2 = d(11).

For k = 3: 2*d(3) = 2*2 = 4 > d(4) = 3.

For k = 2: 2*d(2) = 2*2 = 4 > d(3) = 2.

MATHEMATICA

SequencePosition[DivisorSigma[0, Range[110]], _?(#[[2]]<2#[[1]]&)][[All, 1]]// Quiet (* Harvey P. Dale, Aug 19 2020 *)

PROG

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

CROSSREFS

Cf. A000005, A002808, A063446, A063449.

Sequence in context: A108408 A173905 A171581 * A353684 A377236 A377182

Adjacent sequences: A063447 A063448 A063449 * A063451 A063452 A063453

KEYWORD

nonn,changed

AUTHOR

Labos Elemer, Jul 24 2001

EXTENSIONS

Formatting by Charles R Greathouse IV, Mar 24 2010

STATUS

approved