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A158871 Those positive integers m where (the number of integers k, 0 <= k <= m, where the binomial coefficient C(m,k) is divisible by m) > (the number of positive integers <= m and coprime to m).

%I A158871 #16 May 06 2025 11:19:44
%S A158871 1,10,12,18,20,21,22,24,26,28,30,33,34,35,36,38,39,40,42,44,45,46,48,
%T A158871 50,52,54,55,56,57,58,60,63,65,66,68,69,70,72,74,75,76,77,78,80,82,84,
%U A158871 85,86,87,88,90,92,93,94,96,98,99,100,102,104,105,106,108,110,111,112,114
%N A158871 Those positive integers m where (the number of integers k, 0 <= k <= m, where the binomial coefficient C(m,k) is divisible by m) > (the number of positive integers <= m and coprime to m).
%C A158871 Also numbers m such that A020475(m) > A000010(m).
%C A158871 A020475(n) = the number of integers k, 0 <= k <= n, where the binomial coefficient C(n,k) is divisible by n.
%C A158871 A000010(n) = the number of positive integers <= n and coprime to n.
%C A158871 A020475(n) >= A000010(n) for all positive integers n.
%H A158871 David A. Corneth, <a href="/A158871/b158871.txt">Table of n, a(n) for n = 1..10000</a>
%e A158871 From _David A. Corneth_, May 04 2025: (Start)
%e A158871 12 is in the sequence since 12 | binomial(12, k) for k in {1, 5, 6, 7, 11}. Those are five numbers. A000010(12) = 4 and 5 > 4.
%e A158871 16 is not in the sequence as 16 | binomial(16, k) for k in {1, 3, 5, 7, 9, 11, 13, 15}. Those are 8 numbers. A000010(16) = 8. Those are the same numbers. (End)
%Y A158871 Cf. A000010, A020475.
%K A158871 nonn
%O A158871 1,2
%A A158871 _Leroy Quet_, Mar 28 2009
%E A158871 Extended by _R. J. Mathar_, May 21 2009