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

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, 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, 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

Offset: 1

Author

Antti Karttunen, Mar 20 2017

Keywords

• nonn

Examples

			B_9(x) = x^2 + 2x + 1, which factorizes as (x + 1)^2, thus a(9) = 2^2 = 4.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A046523, A125184, A186891 (positions of terms <= 2), A260443, A277013, A284010, A284012.

Cf. also A278233, A278243.

Differs from A046523 for the first time at n=25, where a(25) = 2, while A046523(25) = 4.

Programs

PARI

\\ After Charles R Greathouse IV's code in A046523 and A186891:
ps(n) = if(n<2, n, if(n%2, ps(n\2)+ps(n\2+1), 'x*ps(n\2)));
A284011(n) = { my(p=0, f=vecsort(factor(ps(n))[, 2], ,4)); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }
for(n=1, 16384, write("b284011.txt", n, " ", A284011(n)));

Formula

a(1) = 1 (by convention), and for n > 1, a(n) = A284010(A260443(n)).