A375229 Numbers k such that A299090(k) is even.

1, 4, 8, 9, 12, 18, 20, 24, 25, 27, 28, 36, 40, 44, 45, 49, 50, 52, 54, 56, 60, 63, 68, 72, 75, 76, 84, 88, 90, 92, 98, 99, 100, 104, 108, 116, 117, 120, 121, 124, 125, 126, 132, 135, 136, 140, 147, 148, 150, 152, 153, 156, 164, 168, 169, 171, 172, 175, 180, 184

Offset: 1

Author

Amiram Eldar, Aug 06 2024

Keywords

• nonn
• easy
• base

Comments

Differs from A252849 by having the terms 1, 256, 512, 768, 1280, ..., and not having the terms 64, 128, 144, 192, 288, ... .

Numbers whose maximum exponent in their unique factorization in terms of distinct "Fermi-Dirac primes" (A368781) is not a power of 4.

The asymptotic density of this sequence is Sum_{k>=1} (1/zeta(4^k) - 1/zeta(2^(2*k-1))) = 0.32005681814901480646... .

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A252849, A299090, A368781.

Programs

Mathematica

q[n_] := EvenQ[IntegerLength[Max[FactorInteger[n][[;; , 2]]], 2]]; q[1] = True; Select[Range[200], q]

PARI

is(n) = if(n == 1, 1, !(#binary(vecmax(factor(n)[, 2])) % 2));