|
|
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.
|
|
1
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|