A197082 Smallest number with n prime divisors (counted with multiplicity) which is not divisible by a(k) for any k < n.

2, 9, 75, 625, 5145, 42875, 352947, 2941225, 28824005, 282475249, 4882786447, 60287465315, 744365643175, 10212696624361, 118890080527911, 1387050939492295, 17125833028425275, 211451611881577375, 2584630720649942503, 30088718564300934153, 351035049916844231785

Offset

1,1

Comments

Conjecture: every proper divisor of a member of this sequence divides infinitely many numbers in the sequence.

Links

Table of n, a(n) for n=1..21.

Example

For a(3), there must be 3 prime divisors. 2 cannot be a divisor, and there can be at most one 3 (otherwise a(1) or a(2) would divide it). The smallest product of three primes subject to these constraints is 3*5*5 = 75.

Prog

(PARI)oddfactfollow(n)={local(fm, np, r);
  fm=factor(n); np=matsize(fm)[1]; r=[];
  if(fm[1, 1]==3, r=concat(r, [n\3*5]);
    if(np>1&&fm[2, 2]==1&&primepi(fm[2, 1])<=lim,
      r=concat(r, [n\fm[2, 1]*nextprime(fm[2, 1]+1)])),
    if(fm[1, 2]==1&&primepi(fm[1, 1])<=lim,
      r=concat(r, [n\fm[1, 1]*nextprime(fm[1, 1]+1)]))); r}
anydiv(v, n, x)=for(k=1, n, if(x%v[k]==0, return(1))); 0
al(n) = {local(r, ms); r=vector(n); r[1]=2;
  for(k=2, n, ms=[3^k];
    while(anydiv(r, k-1, ms[1]),
      ms=vecsort(concat(vector(#ms-1, j, ms[j+1]), oddfactfollow(ms[1]))))
    r[k]=ms[1]);
  r}

Crossrefs

Cf. A001222.

Sequence in context: A015473 A029849 A288581 * A243054 A080638 A370259

Adjacent sequences: A197079 A197080 A197081 * A197083 A197084 A197085

Keyword

nonn

Author

Franklin T. Adams-Watters, Oct 19 2011

Extensions

More terms from D. S. McNeil, Oct 19 2011

Status

approved