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A284011 a(n) = least natural number with the same prime signature Stern polynomial B(n,x) has when it is factored over Z.

%I A284011 #19 Mar 20 2017 23:22:32
%S A284011 1,2,2,4,2,6,2,8,4,6,2,12,2,6,6,16,2,12,2,12,6,6,2,24,2,6,8,12,2,30,2,
%T A284011 32,6,6,6,36,2,6,6,24,2,30,2,12,12,6,2,48,4,6,6,12,2,24,2,24,6,6,2,60,
%U A284011 2,6,30,64,2,30,2,12,6,30,2,72,2,6,12,12,2,30,2,48,6,6,2,60,6,6,6,24,2,60,2,12,6,6,2,96,2,12,12,12,2,30,2,24,30,6,2,72
%N A284011 a(n) = least natural number with the same prime signature Stern polynomial B(n,x) has when it is factored over Z.
%H A284011 Antti Karttunen, <a href="/A284011/b284011.txt">Table of n, a(n) for n = 1..16384</a>
%F A284011 a(1) = 1 (by convention), and for n > 1, a(n) = A284010(A260443(n)).
%e A284011 B_9(x) = x^2 + 2x + 1, which factorizes as (x + 1)^2, thus a(9) = 2^2 = 4.
%o A284011 (PARI)
%o A284011 \\ After _Charles R Greathouse IV_'s code in A046523 and A186891:
%o A284011 ps(n) = if(n<2, n, if(n%2, ps(n\2)+ps(n\2+1), 'x*ps(n\2)));
%o A284011 A284011(n) = { my(p=0, f=vecsort(factor(ps(n))[, 2], ,4)); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }
%o A284011 for(n=1, 16384, write("b284011.txt", n, " ", A284011(n)));
%Y A284011 Cf. A046523, A125184, A186891 (positions of terms <= 2), A260443, A277013, A284010, A284012.
%Y A284011 Cf. also A278233, A278243.
%Y A284011 Differs from A046523 for the first time at n=25, where a(25) = 2, while A046523(25) = 4.
%K A284011 nonn
%O A284011 1,2
%A A284011 _Antti Karttunen_, Mar 20 2017