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

1,2

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

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 *)

Prog

(Scheme with Antti Karttunen's IntSeq-library):
(define A225651 (MATCHING-POS 1 1 (lambda (i) (zero? (modulo (A000793 i) i)))))

Crossrefs

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

Sequence in context: A187966 A280584 A225649 * A191149 A344552 A122907

Adjacent sequences: A225648 A225649 A225650 * A225652 A225653 A225654

Keyword

nonn

Author

Antti Karttunen, May 16 2013

Status

approved