



6, 10, 14, 15, 21, 22, 24, 26, 30, 33, 34, 35, 36, 38, 39, 40, 42, 46, 51, 54, 55, 56, 57, 58, 60, 62, 65, 66, 69, 70, 72, 74, 77, 78, 82, 84, 85, 86, 87, 88, 90, 91, 93, 94, 95, 96, 100, 102, 104, 105, 106, 108, 110, 111, 114, 115, 118, 119, 120, 122, 123, 126, 129, 130, 132, 133, 134, 135, 136, 138, 140, 141
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OFFSET

1,1


COMMENTS

Numbers n such that in their prime factorization n = p_1^e_1 * ... * p_k^e_k, there is at least one pair of exponents e_i and e_j (i and j distinct), such that their base2 representations have at least one shared digitposition in which both exponents have 1bit.


LINKS

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


EXAMPLE

n = 6 = 2^1 * 3^1 is included as both exponents, 1 and 1 ("1" in binary) have both 1bit in position 0 of their binary representations.
n = 24 = 2^3 * 3^1 is included as both exponents, 1 and 3 ("01" and "11" in binary) have both 1bit in position 0 of their binary representations.
n = 36 = 2^2 * 3^2 is included as both exponents, 2 and 2 ("10" in binary) have both 1bit in position 1 of their binary representations.
n = 60 = 2^2 * 3^1 * 5^1 is included as the exponents of 3 and 5, both of which are 1, have both 1bit in position 1 of their binary representations.


MATHEMATICA

Select[Range@ 144, PrimeOmega@ # > BitOr @@ Map[Last, FactorInteger@ #] &] (* Michael De Vlieger, Feb 04 2016 *)


PROG

(Scheme, with Antti Karttunen's IntSeqlibrary)
(define A268376 (NONZEROPOS 1 1 A268374))


CROSSREFS

Cf. A001222, A267116.
Indices of nonzeros in A268374.
Subsequence of A002808 and A024619.
Cf. A268375 (complement).
Cf. A260730 (subsequence).
Cf. also A267117.
Differs from A067582(n+1) for the first time at n=25, where a(n) = 60, a value which is missing from A067582.
Sequence in context: A063763 A115956 A066073 * A067582 A229153 A119847
Adjacent sequences: A268373 A268374 A268375 * A268377 A268378 A268379


KEYWORD

nonn,base


AUTHOR

Antti Karttunen, Feb 03 2016


STATUS

approved



