A382720 Number of entries in the n-th row of Pascal's triangle not divisible by 7.

1, 2, 3, 4, 5, 6, 7, 2, 4, 6, 8, 10, 12, 14, 3, 6, 9, 12, 15, 18, 21, 4, 8, 12, 16, 20, 24, 28, 5, 10, 15, 20, 25, 30, 35, 6, 12, 18, 24, 30, 36, 42, 7, 14, 21, 28, 35, 42, 49, 2, 4, 6, 8, 10, 12, 14, 4, 8, 12, 16, 20, 24, 28, 6, 12, 18, 24, 30, 36, 42, 8, 16, 24, 32, 40, 48, 56, 10, 20, 30, 40

Offset: 0

Author

N. J. A. Sloane, Apr 23 2025

Keywords

• nonn

Links

• Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, Periodic minimum in the count of binomial coefficients not divisible by a prime, arXiv:2408.06817 [math.NT], 2024.

Crossrefs

Cf. A001316, A006047, A194459, A382721-A382722, A382726.

Programs

Mathematica

a[n_] := Times @@ (IntegerDigits[n, 7] + 1);Array[a,81,0] (* James C. McMahon, Aug 16 2025 *)

Python

from math import prod
from gmpy2 import digits
def A382720(n): return prod(int(d)+1 for d in digits(n,7)) # Chai Wah Wu, Aug 10 2025