A374443 - OEIS

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A374443

Triangle read by rows: T(n, k) = rad(gcd(n, k)) if n, k > 0, T(0, 0) = 1, where rad = A007947 and gcd = A109004.

1, 1, 1, 2, 1, 2, 3, 1, 1, 3, 2, 1, 2, 1, 2, 5, 1, 1, 1, 1, 5, 6, 1, 2, 3, 2, 1, 6, 7, 1, 1, 1, 1, 1, 1, 7, 2, 1, 2, 1, 2, 1, 2, 1, 2, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 10, 1, 2, 1, 2, 5, 2, 1, 2, 1, 10, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,4

LINKS

Table of n, a(n) for n=0..90.

EXAMPLE

Triangle starts:

[ 0] 1;

[ 1] 1, 1;

[ 2] 2, 1, 2;

[ 3] 3, 1, 1, 3;

[ 4] 2, 1, 2, 1, 2;

[ 5] 5, 1, 1, 1, 1, 5;

[ 6] 6, 1, 2, 3, 2, 1, 6;

[ 7] 7, 1, 1, 1, 1, 1, 1, 7;

[ 8] 2, 1, 2, 1, 2, 1, 2, 1, 2;

[ 9] 3, 1, 1, 3, 1, 1, 3, 1, 1, 3;

[10] 10, 1, 2, 1, 2, 5, 2, 1, 2, 1, 10;

[11] 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11;

MAPLE

rad := n -> ifelse(n = 0, 1, NumberTheory:-Radical(n)):

T := (n, k) -> rad(igcd(n, k)); seq(seq(T(n, k), k = 0..n), n = 0..11);

MATHEMATICA

rad[n_] := If[n == 0, 1, Product[p, {p, Select[Divisors[n], PrimeQ]}]];

T[n_, k_] := rad[GCD[n, k]]; Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten

CROSSREFS

Variant: A374433.

Cf. A374442 (row sums), A007947, A109004.

Sequence in context: A162319 A237594 A098666 * A362890 A306251 A364027

Adjacent sequences: A374440 A374441 A374442 * A374444 A374445 A374446

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny and Michael De Vlieger, Jul 12 2024

STATUS

approved