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).

1, 10, 12, 18, 20, 21, 22, 24, 26, 28, 30, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, 52, 54, 55, 56, 57, 58, 60, 63, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 82, 84, 85, 86, 87, 88, 90, 92, 93, 94, 96, 98, 99, 100, 102, 104, 105, 106, 108, 110, 111, 112, 114

Offset: 1

Author

Leroy Quet, Mar 28 2009

Keywords

• nonn

Comments

Also numbers m such that A020475(m) > A000010(m).

A020475(n) = the number of integers k, 0 <= k <= n, where the binomial coefficient C(n,k) is divisible by n.

A000010(n) = the number of positive integers <= n and coprime to n.

A020475(n) >= A000010(n) for all positive integers n.

Examples

			From _David A. Corneth_, May 04 2025: (Start)
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.
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)
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A020475.

Extensions

Extended by R. J. Mathar, May 21 2009