A370628 a(n) = GCD(A280864(n), A280864(n+1)).

1, 2, 1, 3, 2, 1, 5, 2, 3, 1, 7, 2, 1, 11, 2, 3, 5, 4, 3, 7, 2, 13, 1, 17, 2, 15, 1, 19, 2, 1, 23, 2, 9, 1, 5, 7, 6, 1, 29, 2, 5, 11, 3, 13, 4, 11, 7, 1, 31, 2, 5, 13, 6, 1, 37, 2, 7, 3, 17, 4, 15, 1, 41, 2, 1, 43, 2, 33, 1, 47, 2, 35, 3, 19, 4, 3, 23, 4, 5

Offset: 1

Author

Rémy Sigrist, May 01 2024

Keywords

• nonn

Examples

			a(89) = GCD(A280864(89), A280864(90)) = GCD(90, 135) = 45.
		

Links

• Rémy Sigrist, PARI program

Crossrefs

Cf. A007947, A280738, A280774, A280864.

Programs

Mathematica

terms = 100;
rad[n_] := Times @@ FactorInteger[n][[All, 1]];
A280864 = Reap[present = 0; p = 1; pp = 1;
    Do[forbidden = GCD[p, pp]; mandatory = p/forbidden;
        a = mandatory;
        While[BitGet[present, a] > 0 || GCD[forbidden, a] > 1,
            a += mandatory];
        Sow[a];
        present += 2^a; pp = p; p = rad[a],
     {terms}]][[2, 1]];
Clear[a];
a[n_] := GCD[A280864[[n]], A280864[[n + 1]]];
Table[a[n], {n, 1, terms - 1}] (* Jean-François Alcover, May 10 2024, adapted from Rémy Sigrist's PARI program *)

PARI

\\ See Links section.

Formula

GCD(a(n), a(n+1)) = 1.

A007947(a(n)) = A280738(n).

a(n) = 1 iff n belongs to A280774.