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A283484 Odd bisection of A283983; square root of the largest square dividing A277324.

%I A283484 #9 Mar 28 2017 14:45:38
%S A283484 1,1,3,1,3,3,15,1,3,15,45,15,15,15,105,1,3,105,225,525,1575,1125,1575,
%T A283484 105,105,525,1575,525,105,105,1155,1,3,1155,1575,3675,7875,275625,
%U A283484 55125,5775,17325,275625,4134375,55125,55125,275625,121275,1155,1155,40425,385875,202125,606375,1929375,606375,5775,8085,40425,121275,40425,1155,1155,15015,1,3
%N A283484 Odd bisection of A283983; square root of the largest square dividing A277324.
%H A283484 Antti Karttunen, <a href="/A283484/b283484.txt">Table of n, a(n) for n = 0..2048</a>
%F A283484 a(n) = A283983((2*n)+1).
%F A283484 a(n) = A000188(A277324(n)).
%F A283484 A001222(a(n)) = A284265(n).
%t A283484 A003961[p_?PrimeQ] := A003961[p] = Prime[ PrimePi[p] + 1]; A003961[1] = 1; A003961[n_] := A003961[n] = Times @@ ( A003961[First[#]] ^ Last[#] & ) /@ FactorInteger[n]  (* after _Jean-François Alcover_, Dec 01 2011 *); A260443[n_]:= If[n<2, n + 1, If[EvenQ[n], A003961[A260443[n/2]], A260443[(n - 1)/2] * A260443[(n + 1)/2]]]; A275812[n_]:= PrimeOmega[n] - If[n<2, 0,Count[Transpose[FactorInteger[n]][[2]], 1]]; A277324[n_]:=A260443[2n + 1];  A000188[n_]:=  Sum[Boole[Mod[i^2, n] == 0], {i, n}]; Table[A000188[A277324[n]], {n, 0, 50}] (* _Indranil Ghosh_, Mar 28 2017 *)
%o A283484 (PARI)
%o A283484 A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From _Michel Marcus_
%o A283484 A260443(n) = if(n<2, n+1, if(n%2, A260443(n\2)*A260443(n\2+1),  A003961(A260443(n\2)))); \\ Cf. _Charles R Greathouse IV_'s code for "ps" in A186891 and A277013.
%o A283484 A277324(n) = A260443((2*n)+1);
%o A283484 A000188(n) = core(n, 1)[2]; \\ This function from _Michel Marcus_, Feb 27 2013
%o A283484 A283484(n) = A000188(A277324(n));
%o A283484 (Scheme)
%o A283484 (define (A283484 n) (A000188 (A277324 n)))
%o A283484 (define (A283484 n) (A283983 (+ n n 1)))
%Y A283484 Cf. A000188, A001222, A277324, A283983, A284265.
%K A283484 nonn
%O A283484 0,3
%A A283484 _Antti Karttunen_, Mar 25 2017