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A375229
Numbers k such that A299090(k) is even.
1
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
1,2
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
MATHEMATICA
q[n_] := EvenQ[IntegerLength[Max[FactorInteger[n][[;; , 2]]], 2]]; q[1] = True; Select[Range[200], q]
PROG
(PARI) is(n) = if(n == 1, 1, !(#binary(vecmax(factor(n)[, 2])) % 2));
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
Amiram Eldar, Aug 06 2024
STATUS
approved