A225651 Numbers k that divide A000793(k).

1, 2, 3, 4, 6, 10, 12, 14, 15, 20, 21, 24, 30, 35, 36, 39, 40, 42, 44, 52, 55, 56, 60, 65, 66, 70, 72, 76, 77, 78, 84, 85, 90, 91, 95, 99, 102, 105, 110, 114, 115, 117, 119, 120, 126, 130, 132, 133, 136, 138, 140, 143, 152, 153, 154, 155, 156, 161, 165, 170

Offset: 1

Author

Antti Karttunen, May 16 2013

Keywords

• nonn

Comments

After 1, a subset of A225649.

Also, for all n, A225650(a(n)) = a(n) and A225655(a(n)) = A000793(a(n)).

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A225648, A225649, A225650, A225653, A225655-A225657.

Programs

Maple

b:= proc(n, i) option remember; local p;
      p:= `if`(i<1, 1, ithprime(i));
      `if`(n=0 or i<1, 1, max(b(n, i-1),
           seq(p^j*b(n-p^j, i-1), j=1..ilog[p](n))))
    end:
g:=n->b(n, `if`(n<8, 3, numtheory[pi](ceil(1.328*isqrt(n*ilog(n)))))):
a:= proc(n) option remember; local k;
      for k from 1+`if`(n=1, 0, a(n-1))
      while not irem(g(k), k)=0 do od; k
    end:
seq(a(n), n=1..70);  # Alois P. Heinz, May 22 2013

Mathematica

Reap[For[n=1, n <= 40, n++, If[Divisible[Max[LCM @@@ IntegerPartitions[n] ], n], Sow[n]]]][[2, 1]]
(* or, for a large number of terms: *)
b[n_, i_] := b[n, i] = Module[{p}, p = If[i<1, 1, Prime[i]]; If[n==0 || i<1, 1, Max[b[n, i-1], Table[p^j*b[n - p^j, i-1], {j, 1, Log[p, n] // Floor}]]]]; g[n_] := b[n, If[n<8, 3, PrimePi[Ceiling[1.328*Sqrt[n*Log[n] // Floor]]]]]; Reap[For[k=1, k <= 1000, k++, If[Divisible[g[k], k], Sow[ k]]]][[2, 1]] (* Jean-François Alcover, Feb 28 2016, after Alois P. Heinz *)