A268388 "Fermi-Dirac composites": numbers k for which A064547(k) > 1.

6, 8, 10, 12, 14, 15, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100, 102, 104, 105, 106, 108, 110, 111, 112, 114, 115, 116, 117, 118, 119, 120

Offset: 1

Author

Antti Karttunen, Feb 09 2016, after Vladimir Shevelev's Apr 2010 comment in A176699

Keywords

• nonn

Examples

			6 = 2^1 * 3^1 is present, as there are altogether two 1-bits in the exponents (1 and 1 also in binary), which is more than one.
64 = 2^6 is present, as the binary representation of 6 is "110", which contains more than one 1-bit. This is also the first term not present in A139118.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A002808.

Cf. A050376 (complement without 1).

Cf. A064547.

Cf. A176699 (subsequence), A000379 (also subsequence, without the initial 1).

Different from A139118.

Programs

Mathematica

Select[Range[120], Plus @@ DigitCount[Last /@ FactorInteger[#], 2, 1] > 1 &] (* Amiram Eldar, Nov 27 2020 *)

PARI

isok(n) = my(f = factor(n)[,2]); sum(k=1, #f, hammingweight(f[k])) > 1; \\ Michel Marcus, Feb 10 2016

Python

from sympy import primepi, integer_nthroot
def A268388(n):
    def f(x): return int(n+1+sum(primepi(integer_nthroot(x,1<Chai Wah Wu, Feb 22 2025