A284011 - OEIS

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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.

9

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

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

FORMULA

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

EXAMPLE

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

PROG

(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)));

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.

Sequence in context: A119655 A364949 A083260 * A275468 A046523 A278524

Adjacent sequences: A284008 A284009 A284010 * A284012 A284013 A284014

KEYWORD

nonn

AUTHOR

Antti Karttunen, Mar 20 2017

STATUS

approved