A300117 Squarefree odd composite numbers n having a prime factor p such that (p-1)|(n-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

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