Original entry on oeis.org
1, 3, 5, 7, 27, 11, 13, 30375, 17, 19, 750141, 23, 3125, 19683, 29, 31, 235782657, 1313046875, 37, 3502727631, 41, 43, 28025208984375, 47, 823543, 634465620819, 53, 7863818359375, 7971951402153, 59, 61, 422112982235053221, 453238525390625
Offset: 0
-
PF := n -> ifelse(n = 0, {}, NumberTheory:-PrimeFactors(n)):
T := (n, k) -> mul(PF(n) intersect PF(k)):
seq(mul(T(2*n+1, k), k = 0..2*n+1), n = 0..20);
-
nn = 65; Do[Set[s[i], FactorInteger[i][[All, 1]]], {i, 0, nn}]; Table[Product[Times @@ Intersection[s[k], s[n]], {k, 0, n}], {n, 1, nn, 2}] (* Michael De Vlieger, Jul 11 2024 *)
A374433
Triangle read by rows: T(n, k) = Product_{p in PF(n) intersect PF(k)} p, where PF(a) is the set of the prime factors of a.
Original entry on oeis.org
1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 5, 1, 1, 2, 3, 2, 1, 6, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 2, 1, 2, 5, 2, 1, 2, 1, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6
Offset: 0
[ 0] 1;
[ 1] 1, 1;
[ 2] 1, 1, 2;
[ 3] 1, 1, 1, 3;
[ 4] 1, 1, 2, 1, 2;
[ 5] 1, 1, 1, 1, 1, 5;
[ 6] 1, 1, 2, 3, 2, 1, 6;
[ 7] 1, 1, 1, 1, 1, 1, 1, 7;
[ 8] 1, 1, 2, 1, 2, 1, 2, 1, 2;
[ 9] 1, 1, 1, 3, 1, 1, 3, 1, 1, 3;
[10] 1, 1, 2, 1, 2, 5, 2, 1, 2, 1, 10;
[11] 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11;
Family: this sequence (intersection),
A374434 (symmetric difference),
A374435 (difference),
A374436 (union).
-
PF := n -> ifelse(n = 0, {}, NumberTheory:-PrimeFactors(n)):
A374433 := (n, k) -> mul(PF(n) intersect PF(k)):
seq(seq(A374433(n, k), k = 0..n), n = 0..12);
-
nn = 12; Do[Set[s[i], FactorInteger[i][[All, 1]]], {i, 0, nn}]; s[0] = {1};
Table[Times @@ Intersection[s[k], s[n]], {n, 0, nn}, {k, 0, n}] // Flatten (* Michael De Vlieger, Jul 11 2024 *)
-
from math import prod
from sympy import primefactors
def PF(n): return set(primefactors(n)) if n > 0 else set({})
def PrimeIntersect(n, k): return prod(PF(n).intersection(PF(k)))
def PrimeSymDiff(n, k): return prod(PF(n).symmetric_difference(PF(k)))
def PrimeUnion(n, k): return prod(PF(n).union(PF(k)))
def PrimeDiff(n, k): return prod(PF(n).difference(PF(k)))
A374433 = PrimeIntersect; A374434 = PrimeSymDiff
A374435 = PrimeDiff; A374436 = PrimeUnion
for n in range(11): print([A374433(n, k) for k in range(n + 1)])
Showing 1-2 of 2 results.
