A362805 Primitive terms of A362804: terms k of A362804 such that k/2 is not a term of A362804.

1, 6, 28, 30, 45, 496, 8128, 16380, 57720, 65472, 235246, 683520, 33550336, 50426880, 60945408, 105553910, 131297280, 3052879872, 8589869056

Offset: 1

Author

Amiram Eldar, May 04 2023

Keywords

• nonn
• base
• more

Comments

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

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

All the even perfect numbers (A000396) are terms.

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

Crossrefs

Subsequence of A362804.

Cf. A000396.

Programs

Mathematica

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

PARI

div(n) = select(x->(bitor(x, n) == n), divisors(n));
is1(n) = {my(d = div(n)); denominator(#d/sum(i = 1, #d ,1/d[i])) == 1;}
is(n) = is1(n) && (n%2 || !is1(n/2));