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%I #12 Mar 28 2017 14:46:06
%S 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,
%T 1225,225,1,11025,1,1,1,9,25,11025,49,50625,1225,275625,121,2480625,
%U 30625,1265625,49,2480625,1225,11025,1,11025,1225,275625,5929,2480625,1225,275625
%N Largest square dividing prime factorization representation of the n-th Stern polynomial: a(n) = A008833(A260443(n)).
%H Antti Karttunen, <a href="/A283989/b283989.txt">Table of n, a(n) for n = 0..1024</a>
%F a(n) = A008833(A260443(n)).
%F a(n) = A260443(n) / A277330(n).
%F a(n) = A283983(n)^2.
%F a(2n) = A003961(a(n)).
%t 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 *)
%o (PARI)
%o A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From _Michel Marcus_
%o 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 A008833(n) = n/core(n); \\ This function from _Michael B. Porter_, Oct 17 2009
%o A283989(n) = A008833(A260443(n));
%o (Scheme)
%o (define (A283989 n) (A008833 (A260443 n)))
%o (define (A283989 n) (/ (A260443 n) (A277330 n)))
%Y Cf. A003961, A008833, A260443, A277330, A283983.
%Y Cf. A023758 (positions of ones).
%K nonn
%O 0,6
%A _Antti Karttunen_, Mar 25 2017
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