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

1,2

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.

Links

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

Example

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)

Crossrefs

Cf. A000010, A020475.

Sequence in context: A270819 A031183 A265043 * A359074 A247626 A247627

Adjacent sequences: A158868 A158869 A158870 * A158872 A158873 A158874

Keyword

nonn

Author

Leroy Quet, Mar 28 2009

Extensions

Extended by R. J. Mathar, May 21 2009

Status

approved