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

1,2

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

Table of n, a(n) for n=1..11.

Index entries for sequences related to binary expansion of n.

Index entries for sequences related to divisors of numbers.

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

Prog

(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)};

Crossrefs

Subsequence of A359080.

Cf. A000005, A246600, A359081, A359082.

Sequence in context: A216757 A218366 A359082 * A218236 A218282 A103454

Adjacent sequences: A359080 A359081 A359082 * A359084 A359085 A359086

Keyword

nonn,base,more

Author

Amiram Eldar, Dec 15 2022

Status

approved