%I #12 Nov 19 2022 04:45:01

%S 1,3,5,7,3,11,13,15,17,19,21,23,5,3,29,31,33,35,37,39,41,43,15,47,7,

%T 51,53,55,57,59,61,21,65,67,69,71,73,15,77,79,3,83,85,87,89,91,93,95,

%U 97,33,101,103,105,107,109,111,113,115,39,119,11,123,5,127,129,131,133,15,137

%N Bisection of A007947.

%H Amiram Eldar, <a href="/A099984/b099984.txt">Table of n, a(n) for n = 1..10000</a>

%F From _Amiram Eldar_, Nov 19 2022: (Start)

%F a(n) = A007947(2*n-1).

%F Sum_{k=1..n} a(k) ~ c * n^2, where c = (6/5) * Product_{p prime} (1 - 1/(p*(p+1))) = (6/5) * A065463 = 0.8453306... . (End)

%p with(numtheory): A007947 := proc(n) local i,t1,t2; t1 :=ifactors(n)[2]; t2 := mul(t1[i][1],i=1..nops(t1)); end: seq(A007947(2*n-1),n=1..78); # _Emeric Deutsch_, Dec 15 2004

%t a[n_] := Times @@ (First /@ FactorInteger[2*n-1]); Array[a, 100] (* _Amiram Eldar_, Nov 19 2022*)

%o (PARI) a(n) = factorback(factorint(2*n-1)[, 1]); \\ _Amiram Eldar_, Nov 19 2022

%Y Cf. A007947, A065463, A099985.

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_, Nov 19 2004

%E More terms from _Emeric Deutsch_, Dec 15 2004

%E Offset corrected by _Amiram Eldar_, Nov 19 2022