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

%I

%S 15,21,33,39,51,57,65,69,85,87,91,93,105,111,123,129,133,141,145,159,

%T 165,177,183,185,195,201,205,213,217,219,231,237,249,255,259,265,267,

%U 273,285,291,301,303,305,309,321,327,339,341,345,357,365,381,385,393,399,411

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

%C 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).

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

%H Charles R Greathouse IV, <a href="/A300117/b300117.txt">Table of n, a(n) for n = 1..10000</a>

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

%t 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 *)

%o (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

%Y Cf. A177516, A002997.

%K nonn

%O 1,1

%A _David James Sycamore_, Feb 25 2018

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Last modified January 27 09:05 EST 2023. Contains 359838 sequences. (Running on oeis4.)