A268388 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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.