
COMMENTS

The corresponding values of m: 10, 4, 6, 10, 4, 10, 4, 10, 7, 4, 10, 6, 10, 10, 8, 10, 7, 10, 100, 34, 12, 55, 28, 19, 40, 14, 22, 28, 16, 25, 19, 13, 18, 20, 19, 16, 11, 100, 34, 70, 24, 55, 37, 28, 19, 46, 26, 40, 28, 22, 19, 30, 28, 16, 100, 34, 28.
This property seems to be very interesting: some primes have it, some don't (from the first 60 primes bigger than 10, 29 have this property and 31 haven't, which is a surprisingly equal proportion); some odd composite numbers have it, some don't (just less than a third from the first 60 such numbers have it), but most of Carmichael numbers checked have it; the first 20 such numbers will be enumerated, with the corresponding value of n in the brackets: 1105(184), 1729(96), 2465(154), 2821(235), 6601(550), 8911(495), 10585(588), 15841(880), 29341(1630), 41041(4560), 46657(1728), 52633(2924), 62745(2728), 101101(33700), 115921(6440), 126217(7012), 172081(9560), 188461(10470), 252601(16840), 294409(10904).
From the first 25 Carmichael numbers, just 5 of them (561, 63973, 75361, 162401 and 278545) lack this property.
