A374609 Numbers k such that k*(k+1) is primorial (a term in A002110).

1, 2, 5, 14, 714

Offset: 1

Author

David James Sycamore and Michael De Vlieger, Jul 13 2024

Keywords

• nonn
• hard

Comments

All terms are squarefree numbers (A005117).

a(n) >> exp(n/2); presumably finite. If a(6) exists then a(6) > 10^200000. - Charles R Greathouse IV, Jul 13 2024

Examples

			714 is a term because 714*715 = 510510 = A002110(7) = 2*3*5*7*11*13*17.
		

Crossrefs

Subsequence of A141399 and A007674.

Cf. A000194, A002110, A002378, A005117, A161620 (resulting primorials).

Programs

Mathematica

nn = 1000; MapIndexed[Set[P[First[#2]], #1] &, FoldList[Times, Prime@ Range[nn]]]; Monitor[Reap[Do[(d = Floor@ Sqrt[#]; If[Divisible[#, d], Sow[d]]) &[P[i]], {i, nn}]][[-1, 1]], i] (* Michael De Vlieger, Jul 14 2024 *)

Formula

From Alois P. Heinz, Jul 13 2024: (Start)

a(n) = A000194(A161620(n)).

A002378(a(n)) = A161620(n). (End)