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

1,1

Links

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

Example

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.

Mathematica

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

Prog

(Scheme, with Antti Karttunen's IntSeq-library)
(define A268388 (MATCHING-POS 1 1 (lambda (n) (> (A064547 n) 1))))
(PARI) isok(n) = my(f = factor(n)[, 2]); sum(k=1, #f, hammingweight(f[k])) > 1; \\ Michel Marcus, Feb 10 2016

Crossrefs

Subsequence of A002808.

Cf. A050376 (complement without 1).

Cf. A064547.

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

Different from A139118.

Sequence in context: A331201 A368459 A050199 * A139118 A089229 A345945

Adjacent sequences: A268385 A268386 A268387 * A268389 A268390 A268391

Keyword

nonn

Author

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

Status

approved