A362805 - OEIS

%I #5 May 05 2023 01:41:58

%S 1,6,28,30,45,496,8128,16380,57720,65472,235246,683520,33550336,

%T 50426880,60945408,105553910,131297280,3052879872,8589869056

%N Primitive terms of A362804: terms k of A362804 such that k/2 is not a term of A362804.

%C If k is a term then k*2^m is a term of A362804 for all m >= 0.

%C The odd terms of A362804 and this sequence are common by definition. Are 1 and 45 the only odd terms?

%C All the even perfect numbers (A000396) are terms.

%C a(20) > 2*10^11, if it exists.

%t q[n_] := IntegerQ[HarmonicMean[Select[Divisors[n], BitAnd[n, #] == # &]]]; Select[Range[10^6], q[#] && (OddQ[#] || ! q[#/2]) &]

%o (PARI) div(n) = select(x->(bitor(x, n) == n), divisors(n));

%o is1(n) = {my(d = div(n)); denominator(#d/sum(i = 1, #d ,1/d[i])) == 1;}

%o is(n) = is1(n) && (n%2 || !is1(n/2));

%Y Subsequence of A362804.

%Y Cf. A000396.

%K nonn,base,more

%O 1,2

%A _Amiram Eldar_, May 04 2023