A140578 - OEIS

A140578

A positive integer n is included if n is the smallest integer in a run of a plural number of consecutive integers all with the same number of divisors.

2, 14, 21, 26, 33, 38, 44, 57, 75, 85, 93, 98, 104, 116, 118, 122, 133, 135, 141, 145, 147, 158, 171, 177, 189, 201, 205, 213, 217, 230, 242, 253, 285, 296, 298, 301, 326, 332, 334, 344, 374, 381, 387, 393, 429, 434, 445, 453, 481, 501, 507, 514, 526, 537, 542

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

OFFSET

1,1

COMMENTS

All terms of this sequence are included in sequence A005237.

LINKS

Table of n, a(n) for n=1..55.

EXAMPLE

d(33) = d(34) = d(35), where d(n) is the number of divisors of n. And since d(32) does not equal d(33), d(33) is the first term of this run of similar values. So 33 is included in this sequence.

MATHEMATICA

(First /@ Select[ Split[ Table[ {DivisorSigma[0, n], n}, {n, 1, 600}], First[#1] == First[#2] &] , Length[#] > 1 &])[[All, 2]] (* Jean-François Alcover, Oct 07 2013 *)

CROSSREFS

Cf. A005237.

Sequence in context: A131221 A138047 A005237 * A052213 A280074 A359745

Adjacent sequences: A140575 A140576 A140577 * A140579 A140580 A140581

KEYWORD

nonn

AUTHOR

Leroy Quet, Jul 05 2008

EXTENSIONS

Extended by Ray Chandler, Jun 25 2009

STATUS

approved