A140128 A positive integer k is included if d(d(k)) = d(d(k+1)), where d(k) is the number of divisors of k.

2, 3, 4, 14, 16, 21, 26, 33, 34, 35, 38, 44, 57, 75, 85, 86, 93, 94, 98, 104, 116, 118, 122, 133, 135, 141, 142, 145, 147, 152, 153, 158, 164, 170, 171, 174, 175, 177, 188, 189, 201, 202, 205, 207, 213, 214, 217, 218, 225, 230, 231, 242, 243, 244, 245, 253, 272

Offset: 1

Author

Leroy Quet, Jun 04 2008

Keywords

• nonn

Examples

			35 has 4 divisors and 4 has 3 divisors. 36 has 9 divisors and 9 has 3 divisors. Since d(d(35)) = d(d(36)) (=3), then 35 is included in the sequence.
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A010553.

A005237 is a subsequence.

Programs

Mathematica

Select[Range[250], DivisorSigma[0, DivisorSigma[0, # ]] == DivisorSigma[0, DivisorSigma[0, # + 1]] &] (* Stefan Steinerberger, Jun 05 2008 *)

PARI

is(k) = numdiv(numdiv(k)) == numdiv(numdiv(k+1)); \\ Amiram Eldar, Apr 16 2024

Formula

For m = 2,3,4,5..., a(m) is the smallest integer > a(m-1) such that A010553(a(m)) = A010553(a(m)+1).

Extensions

More terms from Stefan Steinerberger, Jun 05 2008

a(56)-a(57) from Ray Chandler, Jun 26 2009