A063450 Numbers n such that d(n+1) < 2d(n), 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

1,1

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Example

d(p+1) < 2d(p) holds mainly for composites and the primes 2 and 3. E.g.:
n=10: 2d(10) = 2*4 = 8 > 2 = d(11);
n=3: 2d(3) = 2*2 = 4 > d(4) = 3;
n=2: 2d(2) = 2*2 = 4 > d(3) = 2.

Mathematica

SequencePosition[DivisorSigma[0, Range[110]], _?(#[[2]]<2#[[1]]&)][[All, 1]]// Quiet (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 19 2020 *)

Prog

(PARI) { n=0; for (m=1, 10^9, if (numdiv(m + 1) < 2*numdiv(m), write("b063450.txt", n++, " ", m); if (n==1000, break)) ) } \\ Harry J. Smith, Aug 21 2009

Crossrefs

Cf. A000005, A002808.

Sequence in context: A108408 A173905 A171581 * A353684 A047229 A094229

Adjacent sequences: A063447 A063448 A063449 * A063451 A063452 A063453

Keyword

nonn

Author

Labos Elemer, Jul 24 2001

Extensions

Formatting by Charles R Greathouse IV, Mar 24 2010

Status

approved