A212848 Least prime factor of n-th central trinomial coefficient (A002426).

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

Offset: 0

Author

Jonathan Vos Post, May 28 2012

Keywords

• nonn
• easy

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).

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 0..729

Crossrefs

Cf. A000040, A002426, A020639, A102445, A212791.

Programs

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:
map(lpf @ A002426, [$0..100]); # Robert Israel, Jun 20 2017

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 *)

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

Formula

a(n) = A020639(A002426(n)).