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A076976 Product of the smallest prime divisors of composite numbers between successive primes.

%I A076976 #32 Jan 12 2024 17:42:05
%S A076976 1,2,2,12,2,12,2,12,120,2,120,12,2,12,168,120,2,120,12,2,168,12,120,
%T A076976 1680,12,2,12,2,12,2217600,12,168,2,15840,2,120,168,12,312,120,2,
%U A076976 15840,2,12,2,221760,262080,12,2,12,120,2,18720,264,168,120,2,120,12,2,34272
%N A076976 Product of the smallest prime divisors of composite numbers between successive primes.
%C A076976 From _Bernard Schott_, Apr 09 2020: (Start)
%C A076976 a(n) = 2 iff prime(n) is in A001359 (prime gap=2).
%C A076976 a(n) = 12 iff prime(n) is in A029710 (prime gap=4).
%C A076976 a(n) = 24 * p with p prime >= 5 iff prime(n) is in A031924 (prime gap=6).
%C A076976 a(n) = 2^m * q with q odd >= 3 iff prime(n+1) - prime(n) = 2*m where m = A007814(a(n)). (End)
%H A076976 Robert Israel, <a href="/A076976/b076976.txt">Table of n, a(n) for n = 1..10000</a>
%p A076976 p:= 2:
%p A076976 for i from 1 to 100 do
%p A076976   q:= p; p:= nextprime(p);
%p A076976   A[i]:= mul(min(numtheory:-factorset(i)),i=q+1..p-1);
%p A076976 od:
%p A076976 seq(A[i],i=1..100); # _Robert Israel_, Mar 30 2020
%t A076976 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 A076976 (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 A076976 Cf. A029707 (a(n)=2), A029709 (a(n)=12), A076977.
%Y A076976 Cf. A001359, A029710, A031924.
%K A076976 nonn
%O A076976 1,2
%A A076976 _Amarnath Murthy_, Oct 23 2002
%E A076976 More terms from _Sascha Kurz_, Jan 22 2003