A214932 Number of practical numbers between powers of 2 where the practical numbers are A005153.

1, 1, 2, 2, 6, 8, 15, 25, 52, 89, 166, 299, 551, 1050, 1954, 3737, 7098, 13423, 25262, 48028, 91636, 175204, 334986, 643526, 1240052, 2394026, 4620984, 8946603, 17299096, 33473294, 64874632, 125827199, 243999584, 473735230, 920101286, 1789429184, 3482073702

Offset

0,3

Comments

a(n) appears to be a complete sequence analogous to A036378.

Links

Table of n, a(n) for n=0..36.

Example

a(4) = 6 as there are 4 practical numbers > 16 and <= 32 namely 18, 20, 24, 28, 30 and 32.

Mathematica

PracticalQ[n_] := Module[{f, p, e, prod=1, ok=True}, If[n<1||(n>1&&OddQ[n]), False, If[n==1, True, f=FactorInteger[n]; {p, e}=Transpose[f]; Do[If[p[[i]]>1+DivisorSigma[1, prod], ok=False; Break[]]; prod=prod*p[[i]]^e[[i]], {i, Length[p]}]; ok]]]; Table[Length[Select[Range[2^n + 1, 2^(n + 1)], PracticalQ]],
  {n, 0, 25}](* using T. D. Noe's program A005153 *)

Crossrefs

First differences of A209237.

Cf. A005153, A036378, A322257, A327824.

Sequence in context: A284616 A136513 A365662 * A322132 A054153 A000673

Adjacent sequences: A214929 A214930 A214931 * A214933 A214934 A214935

Keyword

nonn

Author

Frank M Jackson, May 03 2013

Extensions

a(26)-a(36) from Amiram Eldar, May 05 2024

Status

approved