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

%I A370628 #13 May 10 2024 08:50:00
%S A370628 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,
%T A370628 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,
%U A370628 1,41,2,1,43,2,33,1,47,2,35,3,19,4,3,23,4,5
%N A370628 a(n) = GCD(A280864(n), A280864(n+1)).
%H A370628 Rémy Sigrist, <a href="/A370628/a370628.gp.txt">PARI program</a>
%F A370628 GCD(a(n), a(n+1)) = 1.
%F A370628 A007947(a(n)) = A280738(n).
%F A370628 a(n) = 1 iff n belongs to A280774.
%e A370628 a(89) = GCD(A280864(89), A280864(90)) = GCD(90, 135) = 45.
%t A370628 terms = 100;
%t A370628 rad[n_] := Times @@ FactorInteger[n][[All, 1]];
%t A370628 A280864 = Reap[present = 0; p = 1; pp = 1;
%t A370628     Do[forbidden = GCD[p, pp]; mandatory = p/forbidden;
%t A370628         a = mandatory;
%t A370628         While[BitGet[present, a] > 0 || GCD[forbidden, a] > 1,
%t A370628             a += mandatory];
%t A370628         Sow[a];
%t A370628         present += 2^a; pp = p; p = rad[a],
%t A370628      {terms}]][[2, 1]];
%t A370628 Clear[a];
%t A370628 a[n_] := GCD[A280864[[n]], A280864[[n + 1]]];
%t A370628 Table[a[n], {n, 1, terms - 1}] (* _Jean-François Alcover_, May 10 2024, adapted from _Rémy Sigrist_'s PARI program *)
%o A370628 (PARI) \\ See Links section.
%Y A370628 Cf. A007947, A280738, A280774, A280864.
%K A370628 nonn
%O A370628 1,2
%A A370628 _Rémy Sigrist_, May 01 2024