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A268375 Numbers n for which A001222(n) = A267116(n). 10
1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 16, 17, 18, 19, 20, 23, 25, 27, 28, 29, 31, 32, 37, 41, 43, 44, 45, 47, 48, 49, 50, 52, 53, 59, 61, 63, 64, 67, 68, 71, 73, 75, 76, 79, 80, 81, 83, 89, 92, 97, 98, 99, 101, 103, 107, 109, 112, 113, 116, 117, 121, 124, 125, 127, 128, 131, 137, 139, 144, 147, 148, 149, 151, 153 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Numbers n such that in their prime factorization n = p_1^e_1 * ... * p_k^e_k, there are no pair of exponents e_i and e_j (i and j distinct), such that their base-2 representations would have at least one shared digit-position in which both exponents would have 1-bit.

LINKS

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

EXAMPLE

12 = 2^2 * 3^1 is included in the sequence as the exponents 2 ("10" in binary) and 1 ("01" in binary) have no 1-bits in the same position, and 18 = 2^1 * 3^2 is included for the same reason.

On the other hand, 24 = 2^3 * 3^1 is NOT included in the sequence as the exponents 3 ("11" in binary) and 1 ("01" in binary) have 1-bit in the same position 0.

720 = 2^4 * 3^2 * 5^1 is included as the exponents 1, 2 and 4 ("001", "010" and "100" in binary) have no 1-bits in shared positions.

Likewise, 10! = 3628800 = 2^8 * 3^4 * 5^2 * 7^1 is included as the exponents 1, 2, 4 and 8 ("0001", "0010", "0100" and "1000" in binary) have no 1-bits in shared positions. And similarly for any term of A191555.

MATHEMATICA

{1}~Join~Select[Range@ 160, PrimeOmega@ # == BitOr @@ Map[Last, FactorInteger@ #] &] (* Michael De Vlieger, Feb 04 2016 *)

PROG

(Scheme, with Antti Karttunen's IntSeq-library)

(define A268375 (ZERO-POS 1 1 A268374))

CROSSREFS

Indices of zeros in A268374, also in A289618.

Cf. A001222, A267116, A046645, A289617.

Cf. A268376 (complement).

Cf. A000961, A054753, A191555 (subsequences).

Sequence in context: A130091 A119848 A265640 * A048683 A231876 A304686

Adjacent sequences:  A268372 A268373 A268374 * A268376 A268377 A268378

KEYWORD

nonn,base

AUTHOR

Antti Karttunen, Feb 03 2016

STATUS

approved

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Last modified September 16 06:21 EDT 2019. Contains 327090 sequences. (Running on oeis4.)