A283989 Largest square dividing prime factorization representation of the n-th Stern polynomial: a(n) = A008833(A260443(n)).

1, 1, 1, 1, 1, 9, 1, 1, 1, 9, 25, 9, 1, 225, 1, 1, 1, 9, 25, 225, 49, 2025, 25, 225, 1, 225, 1225, 225, 1, 11025, 1, 1, 1, 9, 25, 11025, 49, 50625, 1225, 275625, 121, 2480625, 30625, 1265625, 49, 2480625, 1225, 11025, 1, 11025, 1225, 275625, 5929, 2480625, 1225, 275625

Offset: 0

Author

Antti Karttunen, Mar 25 2017

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..1024

Crossrefs

Cf. A003961, A008833, A260443, A277330, A283983.

Cf. A023758 (positions of ones).

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]]]; A000188[n_]:= Sum[Boole[Mod[i^2, n] == 0], {i, n}]; Table[A000188[A260443[n]]^2, {n, 0, 20}] (* 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.
A008833(n) = n/core(n); \\ This function from Michael B. Porter, Oct 17 2009
A283989(n) = A008833(A260443(n));

Scheme

(define (A283989 n) (A008833 (A260443 n)))
(define (A283989 n) (/ (A260443 n) (A277330 n)))

Formula

a(n) = A008833(A260443(n)).

a(n) = A260443(n) / A277330(n).

a(n) = A283983(n)^2.

a(2n) = A003961(a(n)).