A359083 Numbers k such that A246600(k) = A000005(k) and A000005(k) sets a new record.

1, 3, 15, 63, 255, 891, 4095, 262143, 1048575, 16777215, 68719476735

Offset: 1

Author

Amiram Eldar, Dec 15 2022

Keywords

• nonn
• base
• more

Comments

Numbers k with a record number of divisors, such that for all the divisors d of k the bitwise OR of k and d is equal to k (or equivalently, the bitwise AND of k and d is equal to d).

All the terms are odd since all the terms of A359080 are odd.

The corresponding numbers of divisors are 1, 2, 4, 6, 8, 10, 24, 32, 48, 96, 512, ... .

a(12) > 3*10^11, if it exists.

Links

• Index entries for sequences related to binary expansion of n.
• Index entries for sequences related to divisors of numbers.

Crossrefs

Subsequence of A359080.

Cf. A000005, A246600, A359081, A359082.

Programs

Mathematica

s[n_] := DivisorSum[n, 1 &, BitAnd[n, #] == # &]; seq={}; dm = 0; Do[d = DivisorSigma[0, n]; If[d > dm && d == s[n], dm = d; AppendTo[seq, n]], {n, 1, 2*10^7}]; seq

PARI

lista(nmax) = {my(list = List(), ndmax = 0, d, s); for(n = 1, nmax, nd = numdiv(n); if(nd > ndmax && sumdiv(n, d, bitand(d, n)==d) == nd, ndmax = nd; listput(list, n))); Vec(list)};