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

1,1

Links

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

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).

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A000005, A010553.

A005237 is a subsequence.

Sequence in context: A344313 A103048 A343819 * A167906 A100998 A295286

Adjacent sequences: A140125 A140126 A140127 * A140129 A140130 A140131

Keyword

nonn

Author

Leroy Quet, Jun 04 2008

Extensions

More terms from Stefan Steinerberger, Jun 05 2008

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

Status

approved