A212791 -id:A212791 - cp's OEIS frontend

A212792 Product of all primes in the interval ((n+1)/2,n].

1, 2, 3, 3, 5, 5, 35, 35, 7, 7, 77, 77, 143, 143, 143, 143, 2431, 2431, 46189, 46189, 4199, 4199, 96577, 96577, 7429, 7429, 7429, 7429, 215441, 215441, 6678671, 6678671, 392863, 392863, 392863, 392863, 765049, 765049, 765049, 765049, 31367009, 31367009, 1348781387

Offset: 1

Stanislav Sykora, May 27 2012

nonn

The case n=1 is special and defined conventionally.
a(n) = A034386(n)/A034386(1+floor((n+1)/2)).
Notice that the interval is semiopen; a prime p is included in the product if (n+1)<2p<=2n.

			a(13) = product of all primes in (7,13] = 11*13 = 143.

Stanislav Sykora, Table of n, a(n) for n = 1..1000

Cf. A212791, A034386.

{p2(n) = result=1;forprime(p=1+floor((n+1)\2),n,result=result*p);}

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

Original entry on oeis.org

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

Jonathan Vos Post, May 28 2012

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).

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

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

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

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

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 *)

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

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

cp's OEIS Frontend

A212792 Product of all primes in the interval ((n+1)/2,n].

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