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

1, 1, 3, 1, 3, 3, 15, 1, 3, 15, 45, 15, 15, 15, 105, 1, 3, 105, 225, 525, 1575, 1125, 1575, 105, 105, 525, 1575, 525, 105, 105, 1155, 1, 3, 1155, 1575, 3675, 7875, 275625, 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

Offset: 0

Author

Antti Karttunen, Mar 25 2017

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..2048

Crossrefs

Cf. A000188, A001222, A277324, A283983, A284265.

Programs

Mathematica

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 *)

PARI

A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From Michel Marcus
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.
A277324(n) = A260443((2*n)+1);
A000188(n) = core(n, 1)[2]; \\ This function from Michel Marcus, Feb 27 2013
A283484(n) = A000188(A277324(n));

Scheme

(define (A283484 n) (A000188 (A277324 n)))
(define (A283484 n) (A283983 (+ n n 1)))

Formula

a(n) = A283983((2*n)+1).

a(n) = A000188(A277324(n)).

A001222(a(n)) = A284265(n).