A383276 Numbers of the form A034444(k) * k.

1, 4, 6, 8, 10, 14, 16, 18, 22, 24, 26, 32, 34, 38, 40, 46, 48, 50, 54, 56, 58, 60, 62, 64, 72, 74, 80, 82, 84, 86, 88, 94, 96, 98, 104, 106, 112, 118, 122, 128, 132, 134, 136, 140, 142, 144, 146, 152, 156, 158, 160, 162, 166, 176, 178, 180, 184, 192, 194, 200

Offset: 1

Author

Amiram Eldar, Apr 21 2025

Keywords

• nonn
• easy

Comments

The sorted values of {abs(A298473(n))}.

Numbers m that have a divisor d such that A034444(d) * d = m.

All the terms above 1 are even since A034444(k) is even for k >= 2.

A number m is a term if and only if either A007814(m) = A005087(m) or A007814(m) > A005087(m) + 1.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• H. L. Abbott and M. V. Subbarao, On the Distribution of the Sequence {nd*(n)}, Canadian Mathematical Bulletin, Vol. 32, No. 1 (1989), pp. 105-108.

Crossrefs

The unitary analog of A036438.

Subsequences: A100484, A138929 \ {2}, A151821.

Cf. A005087, A007814, A034444, A298473, A383277 (characteristic function), A383278 (number of terms not exceeding n), A383279.

Programs

Mathematica

q[k_] := AnyTrue[Divisors[k], 2^PrimeNu[#] * # == k &]; Select[Range[200], q]
(* second program: *)
q[k_] := Module[{e = IntegerExponent[k, 2], w}, w = PrimeNu[k/2^e]; e > w + 1 || e == w]; Select[Range[200], q]

PARI

isok(k) = fordiv(k, d, if((1 << omega(d)) * d == k, return(1))); 0;

PARI

isok(k) = {my(e = valuation(k, 2), w = omega(k >> e)); e > w + 1 || e == w;}

Formula

a(n) = A383279(n) * A034444(A383279(n)).