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

Offset: 1

Author

Labos Elemer, Jul 24 2001

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A000005, A002808, A063446, A063449.

Programs

Mathematica

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

PARI

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

Extensions

Formatting by Charles R Greathouse IV, Mar 24 2010