A385748 Numbers k such that A384247(k) divides k.

1, 2, 6, 8, 12, 24, 32, 54, 96, 108, 128, 192, 216, 240, 384, 486, 512, 864, 972, 1536, 1728, 1944, 2048, 2160, 3072, 3456, 4374, 6000, 6144, 7776, 8192, 8748, 13824, 15552, 17496, 19440, 24576, 27648, 31104, 32768, 39366, 49152, 54000, 55296, 61440, 65280, 69984

Offset

1,2

Comments

(2^(2^k)-1) * 2^(2^k) is a term for k = 0..5.

Apparently, the only prime factors of any term are 2 and the Fermat primes (A019434), i.e., A092506.

Apparently, except for n = 1, a(n) / A384247(a(n)) is either 2 or 3.

Links

Amiram Eldar, Table of n, a(n) for n = 1..250

Example

  n | a(n) | a(n) / A384247(a(n))
  --+------+---------------------
  1 |    1 | 1 / 1 = 1
  2 |    2 | 2 / 1 = 2
  3 |    6 | 6 / 2 = 3
  4 |    8 | 8 / 4 = 2
  5 |   12 | 12 / 6 = 2

Mathematica

f[p_, e_] := p^e*(1 - 1/p^(2^(IntegerExponent[e, 2]))); iphi[1] = 1; iphi[n_] := iphi[n] = Times @@ f @@@ FactorInteger[n]; q[n_] := Divisible[n, iphi[n]]; Select[Range[70000], q]

Prog

(PARI) iphi(n) = {my(f = factor(n)); n * prod(i = 1, #f~, (1 - 1/f[i, 1]^(1 << valuation(f[i, 2], 2)))); }
isok(k) = !( k % iphi(k));

Crossrefs

Cf. A019434, A092506, A384247.

Similar sequences: A007694, A298759, A319481, A335327, A373057.

Sequence in context: A082473 A325177 A263312 * A346587 A226818 A113462

Adjacent sequences: A385745 A385746 A385747 * A385749 A385750 A385751

Keyword

nonn

Author

Amiram Eldar, Jul 08 2025

Status

approved