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

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

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.

Mathematica

a[n_] := Times @@ (IntegerDigits[n, 7] + 1); Array[a, 81, 0] (* James C. McMahon, Aug 16 2025 *)
Table[Times@@(IntegerDigits[n, 7]+1), {n, 0, 80}] (* Vincenzo Librandi, Feb 21 2026 *)

Prog

(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
(Magma) [&*[ d+1 : d in (n eq 0 select [0] else IntegerToSequence(n, 7))] : n in [0..70]]; // Vincenzo Librandi, Feb 21 2026

Crossrefs

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

Sequence in context: A240832 A173527 A043267 * A167514 A091733 A066990

Adjacent sequences: A382717 A382718 A382719 * A382721 A382722 A382723

Keyword

nonn

Author

N. J. A. Sloane, Apr 23 2025

Status

approved