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%I #13 Dec 07 2014 18:42:59
%S 11,13,19,21,25,31,37,41,43,49,51,55,61,71,73,81,85,91,101,103,109,
%T 111,113,115,121,127,133,141,145,151,153,157,163,181,191,193,199,201,
%U 205,211,217,221,223,225,229,231,235,241,253,265,267,271,281,289,301,307,309
%N Odd numbers > 10 that can be written as m*s - m + 1, where s is the sum of their digits and m >= 1.
%C 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.
%C 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).
%C From the first 25 Carmichael numbers, just 5 of them (561, 63973, 75361, 162401 and 278545) lack this property.
%H Charles R Greathouse IV, <a href="/A216687/b216687.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CarmichaelNumber.html">Carmichael Number</a>
%o (PARI) is(n)=n%2 && n>9 && Mod(n,sumdigits(n)-1)==1 \\ _Charles R Greathouse IV_, Dec 07 2014
%Y Cf. A002997.
%K nonn,base,easy
%O 1,1
%A _Marius Coman_, Sep 14 2012
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