Descartes number
In number theory, a Descartes number is an odd number which would have been an odd perfect number if one of its composite factors were prime. They are named after René Descartes, who observed that the number D = 32 ⋅ 72 ⋅ 112 ⋅ 132 ⋅ 22021 = (3⋅1001)2 ⋅ (22⋅1001 − 1) = 198585576189 would be an odd perfect number if only 22021 were a prime number, since in that case the sum-of-divisors function for D would satisfy σ ( D ) = ( 3 2 + 3 + 1 ) ⋅ ( 7 2 + 7 + 1 ) ⋅ ( 11 2 + 11 + 1 ) ⋅ ( 13 2 + 13 + 1 ) ⋅ ( 22021 + 1 ) = ( 13 ) ⋅ ( 3 ⋅ 19 ) ⋅ ( 7 ⋅ 19 ) ⋅ ( 3 ⋅ 61 ) ⋅ ( 22 ⋅ 1001 ) = 3 2 ⋅ 7 ⋅ 13 ⋅ 19 2 ⋅ 61 ⋅ ( 22 ⋅ 7 ⋅ 11 ⋅ 13 ) = 2 ⋅ ( 3 2 ⋅ 7 2 ⋅ 11 2 ⋅ 13 2 ) ⋅ ( 19 2 ⋅ 61 ) = 2 ⋅ ( 3 2 ⋅ 7 2 ⋅ 11 2 ⋅ 13 2 ) ⋅ 22021 = 2 D .