A374435 Triangle read by rows: T(n, k) = Product_{p in PF(n) difference PF(k)} p, where PF(a) is the set of the prime factors of a.

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

Offset

0,4

Links

Table of n, a(n) for n=0..77.

Example

  [ 0]  1;
  [ 1]  1,  1;
  [ 2]  2,  2,  1;
  [ 3]  3,  3,  3,  1;
  [ 4]  2,  2,  1,  2,  1;
  [ 5]  5,  5,  5,  5,  5,  1;
  [ 6]  6,  6,  3,  2,  3,  6,  1;
  [ 7]  7,  7,  7,  7,  7,  7,  7,  1;
  [ 8]  2,  2,  1,  2,  1,  2,  1,  2,  1;
  [ 9]  3,  3,  3,  1,  3,  3,  1,  3,  3,  1;
  [10] 10, 10,  5, 10,  5,  2,  5, 10,  5, 10,  1;
  [11] 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 1;

Maple

PF := n -> ifelse(n = 0, {}, NumberTheory:-PrimeFactors(n)):
A374435 := (n, k) -> mul(PF(n) minus PF(k)):
seq(print(seq(A374435(n, k), k = 0..n)), n = 0..11);

Mathematica

nn = 12; Do[Set[s[i], FactorInteger[i][[All, 1]]], {i, 0, nn}]; s[0] = {1}; Table[Apply[Times, Complement[s[n], s[k]]], {n, 0, nn}, {k, 0, n}] // Flatten (* Michael De Vlieger, Jul 11 2024 *)

Prog

(Python)  # Function A374435 defined in A374433.
for n in range(12): print([A374435(n, k) for k in range(n + 1)])

Crossrefs

Family: A374433 (intersection), A374434 (symmetric difference), this sequence (difference), A374436 (union).

Cf. A007947 (column 0), A000034 (central terms).

Sequence in context: A327035 A177352 A210798 * A117501 A117915 A294453

Adjacent sequences: A374432 A374433 A374434 * A374436 A374437 A374438

Keyword

nonn,tabl

Author

Peter Luschny, Jul 10 2024

Status

approved