A207041 Carmichael numbers that can be written as a product of two Carmichael numbers.

509033161, 1836304561, 5394826801, 20064165121, 25594002721, 47782272385, 59970791881, 75527369281, 84127131361, 96578912521, 116087568961, 278585544601, 387394248241, 416937760921, 584698468861, 1623222276481, 1690000282321, 1788750684721, 1945024664401

Offset

1,1

Comments

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

Links

Donovan Johnson and Charles R Greathouse IV, Table of n, a(n) for n = 1..5308 (terms < 2^64; indices 1..2008, representing terms < 10^18, are from Johnson)

Richard Pinch, Carmichael numbers < 10^18

Example

a(1) = 509033161 = 1729 * 294409 = A002997(3) * A002997(25).
a(9) = 84127131361 = 15841 * 5310721 = A002997(9) * A002997(78) = 172081 * 488881 = A002997(21) * A002997(32) (two representations).

Mathematica

(*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]

Crossrefs

Cf. A002997.

Sequence in context: A210155 A348798 A203261 * A339551 A319937 A186092

Adjacent sequences: A207038 A207039 A207040 * A207042 A207043 A207044

Keyword

nonn

Author

Emmanuel Vantieghem, Feb 14 2012

Status

approved