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

1,2

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.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..2261

Rémy Sigrist, C++ program for A293780

Example

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

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 *)

Prog

(C++) See Links section.
(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

Crossrefs

Cf. A007913, A008479, A055932, A293781.

Sequence in context: A123857 A217313 A101434 * A048168 A175341 A317705

Adjacent sequences: A293777 A293778 A293779 * A293781 A293782 A293783

Keyword

nonn

Author

David A. Corneth, Oct 19 2017

Status

approved