

A212848


Least prime factor of nth central trinomial coefficient (A002426).


1



1, 1, 3, 7, 19, 3, 3, 3, 3, 43, 7, 3, 113, 73, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 17, 3, 719, 7, 3, 3, 3, 3, 967, 9539, 3, 17, 47, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 19
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OFFSET

0,3


COMMENTS

A002426(n) is prime for n = 2, 3, 4, no more through 10^5. A002426 is semiprime iff A102445(n) = 2 (as is the case for n = 5, 6, 7, 9, 10, 12, 13).


LINKS



FORMULA



EXAMPLE

a(9) = 43 because A002426(9) = 3139 = 43 * 73.


MAPLE

A002426:= gfun:rectoproc({(n+2)*a(n+2)(2*n+3)*a(n+1)3*(n+1)*a(n) = 0, a(0)=1, a(1)=1}, a(n), remember):
lpf:= proc(n) local F;
F:= map(proc(t) if t[1]::integer then t[1] else NULL fi end proc,
ifactors(n, easy)[2]);
if nops(F) > 0 then min(F)
else min(numtheory:factorset(n))
fi
end proc:
lpf(1):= 1:


MATHEMATICA

a = b = 1; t = Join[{a, b}, Table[c = ((2 n  1) b + 3 (n  1) a)/n; a = b; b = c; c, {n, 2, 100}]]; Table[FactorInteger[n][[1, 1]], {n, t}] (* T. D. Noe, May 30 2012 *)


PROG

(PARI) a(n) = my(x=polcoeff((1 + x + x^2)^n, n)); if (x==1, 1, vecmin(factor(x)[, 1])); \\ Michel Marcus, Jun 20 2017


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



