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A278961 Triangle read by rows: row n consists of k, 1<=k<=n, such that binomial(n,k) is divisible by gcd(n,k). 2
1, 1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 5, 1, 2, 3, 4, 5, 6, 1, 2, 3, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7, 8, 1, 3, 4, 6, 7, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 5, 6, 7, 10, 11, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 3, 5, 9, 11, 13, 1, 2, 4, 7, 8, 11, 13, 14, 1, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
All k coprime to n are always included, in particular 1 and n-1.
Row n contains k if and only if it contains n-k.
A014847 consists of k such that row 2k contains k.
If n is prime or the square of a prime, row n contains all numbers from 1 to n-1. This is not true for higher powers: row p^r does not contain any multiples of p^(r-1) if r > 2.
Prime p is in row n>p if and only if the p-adic order of n is not 1.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10029(rows 1 to 155 flattened)
EXAMPLE
Row 8 contains 2 because gcd(8,2)=2 divides binomial(8,2) = 28, but not 4 because gcd(8,4)=4 does not divide binomial(8,4)= 70.
MAPLE
f:= proc(n, m) if binomial(n, m) mod igcd(n, m) = 0 then m else NULL fi end proc:
seq(seq(f(n, m), m=1..n), n=1..40);
MATHEMATICA
Table[If[Divisible[Binomial[n, k], GCD[n, k]], k, Nothing], {n, 20}, {k, n}]//Flatten (* Harvey P. Dale, Dec 04 2022 *)
CROSSREFS
Cf. A014847.
Sequence in context: A066019 A051237 A064379 * A194973 A195113 A120418
KEYWORD
nonn,tabf
AUTHOR
Robert Israel, Dec 02 2016
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)