A207041 - OEIS

%I #19 Apr 01 2020 09:25:02

%S 509033161,1836304561,5394826801,20064165121,25594002721,47782272385,

%T 59970791881,75527369281,84127131361,96578912521,116087568961,

%U 278585544601,387394248241,416937760921,584698468861,1623222276481,1690000282321,1788750684721,1945024664401

%N Carmichael numbers that can be written as a product of two Carmichael numbers.

%C Subsequence of A002997; a(1) = A002997(472) and a(9) = A002997(3380).

%H Donovan Johnson and Charles R Greathouse IV, <a href="/A207041/b207041.txt">Table of n, a(n) for n = 1..5308</a> (terms < 2^64; indices 1..2008, representing terms < 10^18, are from Johnson)

%H Richard Pinch, <a href="http://s369624816.websitehome.co.uk/rgep/cartable.html">Carmichael numbers < 10^18</a>

%e a(1) = 509033161 = 1729 * 294409 = A002997(3) * A002997(25).

%e a(9) = 84127131361 = 15841 * 5310721 = A002997(9) * A002997(78) = 172081 * 488881 = A002997(21) * A002997(32) (two representations).

%t (*M is the set of the first G (G<=10000) Carmichael numbers, as found in https://oeis.org/A002997/b002997.txt*) i=0; SPCM={}; While[i<G-1,i++;m=M[[i]]; j=i; While[j<G,j++; n=M[[j]]; If[GCD[m,n]==1,c=m n; If[c<=M[[1]] M[[G]],Fc=FactorInteger[c]; k=Length[Fc];j2=0; While[j2<k,j2++; p=First[Fc[[j2]]]; If[Mod[c-1,p-1]!=0,j2=k+1]]; If[j2!=k+1,SPCM=Append[SPCM,c]]]]]]; SPCM=Union[SPCM]

%Y Cf. A002997.

%K nonn

%O 1,1

%A _Emmanuel Vantieghem_, Feb 14 2012