cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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.

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%I A374435 #12 Jul 13 2024 10:12:47
%S A374435 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,
%T A374435 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,
%U A374435 11,11,11,11,11,11,11,11,11,11,11,1
%N 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.
%e A374435   [ 0]  1;
%e A374435   [ 1]  1,  1;
%e A374435   [ 2]  2,  2,  1;
%e A374435   [ 3]  3,  3,  3,  1;
%e A374435   [ 4]  2,  2,  1,  2,  1;
%e A374435   [ 5]  5,  5,  5,  5,  5,  1;
%e A374435   [ 6]  6,  6,  3,  2,  3,  6,  1;
%e A374435   [ 7]  7,  7,  7,  7,  7,  7,  7,  1;
%e A374435   [ 8]  2,  2,  1,  2,  1,  2,  1,  2,  1;
%e A374435   [ 9]  3,  3,  3,  1,  3,  3,  1,  3,  3,  1;
%e A374435   [10] 10, 10,  5, 10,  5,  2,  5, 10,  5, 10,  1;
%e A374435   [11] 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 1;
%p A374435 PF := n -> ifelse(n = 0, {}, NumberTheory:-PrimeFactors(n)):
%p A374435 A374435 := (n, k) -> mul(PF(n) minus PF(k)):
%p A374435 seq(print(seq(A374435(n, k), k = 0..n)), n = 0..11);
%t A374435 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 *)
%o A374435 (Python)  # Function A374435 defined in A374433.
%o A374435 for n in range(12): print([A374435(n, k) for k in range(n + 1)])
%Y A374435 Family: A374433 (intersection), A374434 (symmetric difference), this sequence (difference), A374436 (union).
%Y A374435 Cf. A007947 (column 0), A000034 (central terms).
%K A374435 nonn,tabl
%O A374435 0,4
%A A374435 _Peter Luschny_, Jul 10 2024