A293780 Where records occur in A008479.

1, 4, 8, 16, 32, 48, 54, 72, 96, 108, 144, 162, 192, 216, 288, 324, 384, 432, 486, 576, 648, 768, 864, 972, 1152, 1296, 1458, 1536, 1728, 1944, 2304, 2592, 2880, 3000, 3240, 3600, 3750, 3840, 4050, 4320, 4500, 4800, 4860, 5400, 5760, 6000, 6480, 6750, 7200, 7290, 7500

Offset: 1

Author

David A. Corneth, Oct 19 2017

Keywords

• nonn

Comments

Also values m such that A008479(k) < A008479(m) for all k < m.

Is the squarefree part of a(n); A007913(a(n)) a product of the first primes?

The sequence omega(a(n)) is not nondecreasing; a(1641) and a(1651) are both 7-smooth but a(1640) and a(1650) are divisible by 11.

Is A008479(a(n)) = n?

The least a(n) such that omega(a(n)) gives a record is 4, 48, 2880, 504210, 616319550, 317433916800.

Examples

			8 is in the sequence as A008479(k) < A008479(8) for k < 8.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..2261
• Rémy Sigrist, C++ program for A293780

Crossrefs

Cf. A007913, A008479, A055932, A293781.

Programs

Mathematica

Block[{s = {1}~Join~Array[Times @@ FactorInteger[#][[All, 1]] &, 10^4, 2], t}, t = 1 + Array[Count[Take[s, # - 1], s[[#]]] &, Length@ s]; Map[FirstPosition[t, #][[1]] &, Union@ FoldList[Max, t]] ] (* Michael De Vlieger, Oct 21 2017 *)

PARI

lista(nn) = {nbm = 0; v = vector(nn, k, factor(k)[,1]); for (n=1, nn, vn = vector(n, k, v[k]); nbn = #select(x->(x==v[n]), vn); if (nbn > nbm, print1(n, ", "); nbm = nbn););} \\ Michel Marcus, Oct 30 2017