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

1,2

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

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 *)

Prog

(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

Crossrefs

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

Cf. A001359, A029710, A031924.

Sequence in context: A095215 A264712 A217094 * A291757 A286464 A058044

Adjacent sequences: A076973 A076974 A076975 * A076977 A076978 A076979

Keyword

nonn

Author

Amarnath Murthy, Oct 23 2002

Extensions

More terms from Sascha Kurz, Jan 22 2003

Status

approved