login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A300117 Squarefree odd composite numbers n having a prime factor p such that (p-1)|(n-1). 1
15, 21, 33, 39, 51, 57, 65, 69, 85, 87, 91, 93, 105, 111, 123, 129, 133, 141, 145, 159, 165, 177, 183, 185, 195, 201, 205, 213, 217, 219, 231, 237, 249, 255, 259, 265, 267, 273, 285, 291, 301, 303, 305, 309, 321, 327, 339, 341, 345, 357, 365, 381, 385, 393, 399, 411 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A177516 is a subsequence since each of its terms is a semiprime n=p*q; p<q, and (p-1)|(q-1) ==> (p-1)|(n-1).

A002997 is also a subsequence (by definition), and a(81)=A002997(1), the first Carmichael number.

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

EXAMPLE

15 is included because 2|14, 105 is included because 4|104.

MATHEMATICA

Select[Range@ 600, Function[n, And[SquareFreeQ@ n, OddQ@ n, CompositeQ@ n, AnyTrue[FactorInteger[n][[All, 1]], Divisible[n - 1, # - 1] &]]]] (* Michael De Vlieger, Feb 25 2018 *)

PROG

(PARI) list(lim)=my(v=List()); forsquarefree(n=3, lim\1, if(n[2][1, 1]==2 || #n[2][, 2]==1, next); for(i=1, #n[2][, 2], if((n[1]-1)%(n[2][i, 1]-1)==0, listput(v, n[1]); break))); Vec(v) \\ Charles R Greathouse IV, Feb 25 2018

CROSSREFS

Cf. A177516, A002997.

Sequence in context: A020162 A046404 A198680 * A214044 A177516 A127329

Adjacent sequences: A300114 A300115 A300116 * A300118 A300119 A300120

KEYWORD

nonn

AUTHOR

David James Sycamore, Feb 25 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 1 23:44 EST 2022. Contains 358485 sequences. (Running on oeis4.)