A249435 -id:A249435 - cp's OEIS frontend

A249433 Integers n such that n! does not divide the product of elements on row n of Pascal's triangle.

3, 5, 7, 8, 9, 11, 13, 14, 15, 17, 19, 20, 21, 23, 24, 25, 26, 27, 29, 31, 32, 33, 34, 37, 38, 41, 43, 44, 45, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 59, 61, 63, 64, 65, 67, 68, 69, 71, 73, 74, 75, 76, 77, 80, 81, 84, 85, 86, 87, 90, 91, 92, 93, 94, 95, 97, 98, 99, 101, 103, 105, 109, 110, 111, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 127, 128

Offset: 1

Antti Karttunen, Nov 02 2014

nonn

Integers n such that A249151(n) < n.

Equally: Integers n such that A249431(n) is negative.

			See the examples at A249434.

Antti Karttunen, Table of n, a(n) for n = 1..2676

Complement: A249434.
Subsequences: A000225, A024023, A024049, etc., (after their two initial terms, i.e. A249435 without its initial zero is also a subsequence), A249424, A249436.
Cf. A000142, A001142, A007318, A249151, A249431.

A372305 a(n) = Product_{k=2..n-1} MultiplicativeOrder(k,n) where gcd(k,n)=1.

Original entry on oeis.org

1, 1, 2, 2, 32, 2, 648, 8, 648, 32, 12500000, 8, 214990848, 648, 2048, 2048, 562949953421312, 648, 11712917736940032, 2048, 3359232, 12500000, 1377791989621882898843648, 128, 5120000000000000000, 214990848, 11712917736940032

Offset: 1

Darío Clavijo, Apr 25 2024

nonn

All terms are even for n>=3.

Cf. A000079, A036391, A249435.

Row products of triangle A216327.

Table[Times @@ Map[MultiplicativeOrder[#, n] &, Select[Range[2, n - 1], CoprimeQ[n, #] &]], {n, 2, 27}] (* Michael De Vlieger, Apr 25 2024 *)

a(n) = prod(k=2, n-1, if (gcd(k,n)==1, znorder(Mod(k,n)), 1)); \\ Michel Marcus, Apr 26 2024

from sympy import n_order, gcd, prod
a = lambda n: prod(n_order(k,n) for k in range(2, n) if gcd(k,n)==1)
print([a(n) for n in range(1, 28)])

cp's OEIS Frontend

A249433 Integers n such that n! does not divide the product of elements on row n of Pascal's triangle.

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A372305 a(n) = Product_{k=2..n-1} MultiplicativeOrder(k,n) where gcd(k,n)=1.

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