A257146 Primitive non-solvable numbers: elements of A056866 not divisible by any earlier term.

60, 168, 1092, 2448, 5616, 6072, 25308, 29120, 32736, 39732, 51888, 74412, 150348, 194472, 285852, 546312, 612468, 1285608, 1934868, 2097024, 2165292, 2588772, 3594432, 3822588, 5848428, 6324552, 7174332, 8487168, 9095592, 10626828, 11332452, 12576732, 14467068, 15331992, 15927348

Offset: 1

Author

Charles R Greathouse IV, Apr 16 2015

Keywords

• nonn

Comments

A number is solvable if and only if it is a positive multiple of a member of this sequence.

There is 1 member of this sequence up to 10^2, 2 up to 10^3, 6 up to 10^4, 12 up to 10^5, 17 up to 10^6, 29 up to 10^7, 49 up to 10^8, 89 up to 10^9, 169 up to 10^10, 321 up to 10^11, 616 up to 10^12, 1188 up to 10^13, 2351 up to 10^14, 4679 up to 10^15, 9350 up to 10^16, 18866 up to 10^17, 38157 up to 10^18, 77534 up to 10^19, 158048 up to 10^20, 323358 up to 10^21, 663159 up to 10^22, and 1363304 up to 10^23. - Charles R Greathouse IV, Sep 16 2015

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A056866.

Programs

PARI

list(lim)={
  my(v=List(),t);
  forprime(p=2,,
    t=(4^p-1)<lim,break);
    listput(v,t)
  );
  forprime(p=3,,
    t=3^p*(9^p-1)/2;
    if(t>lim,break);
    listput(v,t)
  );
  forprime(p=7,,
    t=p*(p^2-1)/2;
    if(t>lim,break);
    listput(v,t)
  );
  forprime(p=3,,
    t=4^p*(4^p+1)*(2^p-1);
    if(t>lim,break);
    listput(v,t)
  );
  if(lim>=5616, listput(v, 5616));
  v=Set(v);
  for(i=1,#v,
    if(v[i]==60 && i>1, next); \\ see below
    for(j=i+1,#v,
      if(v[j]%v[i]==0, v[j]=60) \\ delete values by setting to v[1]
    )
  );
  Set(v); \\ remove duplicates to combine all 60s
}

Formula

a(n) >> n^3 log^3 n. - Charles R Greathouse IV, Apr 20 2015