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

1, 2, 2, 12, 2, 12, 2, 12, 120, 2, 120, 12, 2, 12, 168, 120, 2, 120, 12, 2, 168, 12, 120, 1680, 12, 2, 12, 2, 12, 2217600, 12, 168, 2, 15840, 2, 120, 168, 12, 312, 120, 2, 15840, 2, 12, 2, 221760, 262080, 12, 2, 12, 120, 2, 18720, 264, 168, 120, 2, 120, 12, 2, 34272

Offset: 1

Author

Amarnath Murthy, Oct 23 2002

Keywords

• nonn

Comments

From Bernard Schott, Apr 09 2020: (Start)

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

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

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

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

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

Cf. A001359, A029710, A031924.

Programs

Maple

p:= 2:
for i from 1 to 100 do
  q:= p; p:= nextprime(p);
  A[i]:= mul(min(numtheory:-factorset(i)),i=q+1..p-1);
od:
seq(A[i],i=1..100); # Robert Israel, Mar 30 2020

Mathematica

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 *)

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

Extensions

More terms from Sascha Kurz, Jan 22 2003