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%I #18 Aug 04 2016 14:24:08
%S 1,6,10,12,14,15,18,20,21,22,24,26,28,33,34,35,36,38,39,40,44,45,46,
%T 48,50,51,52,54,55,56,57,58,62,63,65,68,69,72,74,75,76,77,80,82,85,86,
%U 87,88,91,92,93,94,95,96,98,99,100,104,106,108,111,112,115,116,117,118,119,122,123,124,129,133,134,135,136,141,142,143,144
%N Numbers n for which A001222(n) = A267115(n) + A267116(n).
%H Antti Karttunen, <a href="/A267114/b267114.txt">Table of n, a(n) for n = 1..10000</a>
%e 6 = 2^1 * 3^1 is included as bitwise-or of its exponents is 1 and likewise bitwise-and(1,1) = 1 and 1+1 = A001222(6) = 2, the number of the prime factors of 6 when counted with multiplicity.
%e 12 = 2^2 * 3^1 is included as bitwise-or of its exponents ("10" and "01" in binary) is 3 ("11"), bitwise-and(1,2) = 0 and 3+0 = A001222(12).
%e 60 = 2^2 * 3^1 * 5^1 is NOT included as bitwise-or(2,1,1) = 3, bitwise-and(2,1,1) = 0 and 3+0 < 4 = A001222(60).
%t {1}~Join~Select[Range@ 144, Function[n, PrimeOmega@ n == BitAnd @@ # + BitOr @@ # &@ Map[Last, FactorInteger@ n]]] (* _Michael De Vlieger_, Feb 07 2016 *)
%o (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o (define A267114 (ZERO-POS 1 1 (lambda (n) (- (A001222 n) (+ (A267115 n) (A267116 n))))))
%o (PARI) is(n)=if(n>1, my(f=factor(n)[,2]); fold(bitand, f) + fold(bitor, f) == vecsum(f), 1) \\ _Charles R Greathouse IV_, Aug 04 2016
%Y Cf. A001222, A267115, A267116, A267117.
%Y Differs from A030231 for the first time at n=118, where A030231(118) = 210 (= 2*3*5*7), which term is missing from this sequence.
%Y a(n+1) differs from A007774 for the first time at n=375, as a(376) = 720 = 2^4 * 3^2 * 5^1.
%Y Cf. A007774 (subsequence).
%K nonn
%O 1,2
%A _Antti Karttunen_, Feb 03 2016
%E Erroneous claim corrected by _Antti Karttunen_, Feb 07 2016
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