A267114 Numbers n for which A001222(n) = A267115(n) + A267116(n).

1, 6, 10, 12, 14, 15, 18, 20, 21, 22, 24, 26, 28, 33, 34, 35, 36, 38, 39, 40, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 57, 58, 62, 63, 65, 68, 69, 72, 74, 75, 76, 77, 80, 82, 85, 86, 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

Offset: 1

Author

Antti Karttunen, Feb 03 2016

Keywords

• nonn

Examples

			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.
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).
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).
		

Links

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

Crossrefs

Cf. A001222, A267115, A267116, A267117.

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.

a(n+1) differs from A007774 for the first time at n=375, as a(376) = 720 = 2^4 * 3^2 * 5^1.

Cf. A007774 (subsequence).

Programs

Mathematica

{1}~Join~Select[Range@ 144, Function[n, PrimeOmega@ n == BitAnd @@ # + BitOr @@ # &@ Map[Last, FactorInteger@ n]]] (* Michael De Vlieger, Feb 07 2016 *)

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

Extensions

Erroneous claim corrected by Antti Karttunen, Feb 07 2016