A076976 - OEIS

%I #32 Jan 12 2024 17:42:05

%S 1,2,2,12,2,12,2,12,120,2,120,12,2,12,168,120,2,120,12,2,168,12,120,

%T 1680,12,2,12,2,12,2217600,12,168,2,15840,2,120,168,12,312,120,2,

%U 15840,2,12,2,221760,262080,12,2,12,120,2,18720,264,168,120,2,120,12,2,34272

%N Product of the smallest prime divisors of composite numbers between successive primes.

%C From _Bernard Schott_, Apr 09 2020: (Start)

%C a(n) = 2 iff prime(n) is in A001359 (prime gap=2).

%C a(n) = 12 iff prime(n) is in A029710 (prime gap=4).

%C a(n) = 24 * p with p prime >= 5 iff prime(n) is in A031924 (prime gap=6).

%C a(n) = 2^m * q with q odd >= 3 iff prime(n+1) - prime(n) = 2*m where m = A007814(a(n)). (End)

%H Robert Israel, <a href="/A076976/b076976.txt">Table of n, a(n) for n = 1..10000</a>

%p p:= 2:

%p for i from 1 to 100 do

%p   q:= p; p:= nextprime(p);

%p   A[i]:= mul(min(numtheory:-factorset(i)),i=q+1..p-1);

%p od:

%p seq(A[i],i=1..100); # _Robert Israel_, Mar 30 2020

%t pspd[{p1_,p2_}]:=Times@@(FactorInteger[#][[1,1]]&/@Range[p1+1,p2-1]); pspd/@Partition[ Prime[Range[70]],2,1] (* _Harvey P. Dale_, Jan 12 2024 *)

%o (PARI) a(n) = {my(p=1, pn=prime(n)); forcomposite(c=pn, nextprime(pn+1)-1, p *= vecmin(factor(c)[,1]);); p;} \\ _Michel Marcus_, Mar 31 2020

%Y Cf. A029707 (a(n)=2), A029709 (a(n)=12), A076977.

%Y Cf. A001359, A029710, A031924.

%K nonn

%O 1,2

%A _Amarnath Murthy_, Oct 23 2002

%E More terms from _Sascha Kurz_, Jan 22 2003