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A235050 Squarefree numbers such that none of their prime factors share common 1-bits in the same bit-position of their binary representations. 4

%I #13 Feb 01 2014 14:53:07

%S 1,2,3,5,7,10,11,13,17,19,23,26,29,31,34,37,41,43,47,53,58,59,61,67,

%T 71,73,74,79,82,83,89,97,101,103,106,107,109,113,122,127,131,137,139,

%U 146,149,151,157,163,167,173,178,179,181,191,193,194,197,199,202,211,218,223,226,227,229,233,239,241,251,257

%N Squarefree numbers such that none of their prime factors share common 1-bits in the same bit-position of their binary representations.

%C a(1)=1 is included on the grounds that it has no prime factors at all, thus no conflicting 1-bits.

%C After a(1)=1 all n such that A001414(n) = A072593(n), or equally, A001414(n) = A072594(n).

%C Union of noncomposites (A008578) and semiprimes of the form 2*A002144 (cf. also A235490).

%H Antti Karttunen, <a href="/A235050/b235050.txt">Table of n, a(n) for n = 1..10000</a>

%o (Scheme, with _Antti Karttunen_'s IntSeq-library)

%o (define A235050 (MATCHING-POS 1 1 (lambda (n) (or (= 1 n) (= (A001414 n) (A072593 n))))))

%Y Subsequences: A000040, A235490.

%Y Subsequence of A005117.

%Y Cf. also A001414, A072593, A072594, A235040.

%K nonn,easy

%O 1,2

%A _Antti Karttunen_, Jan 22 2014

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