A359082 Indices of records in A246600.

1, 3, 15, 63, 255, 495, 4095, 96255, 98175, 130815, 203775, 1048575, 5810175, 6455295, 16777215, 67096575, 88062975, 389656575, 553517055, 850917375, 1157349375, 9141354495, 12826279935, 22828220415, 26818379775, 31684427775, 68719476735, 242870910975, 1168231038975

Offset

1,2

Comments

Numbers k with a record number of divisors d such that 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 A246600(2*k) = A246600(k).

This sequence is infinite since A246600(2^m-1) = A000005(2^m-1) = A046801(m), and A046801 is unbounded (A046801(2^(m+1)) > A046801(2^m) for all m >= 0).

The corresponding record values are 1, 2, 4, 6, 8, 11, 24, 25, 28, 32, 35, 48, 56, 89, 96, 105, 121, 127, 148, 162, 216, 243, 245, 256, 319, 358, 512, 633, 768, ... .

2*10^11 < a(28) <= 2^48 - 1.

Links

Martin Ehrenstein, Table of n, a(n) for n = 1..36

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={}; sm = 0; Do[If[(sn = s[n]) > sm, sm = sn; AppendTo[seq, n]], {n, 1, 10^6}]; seq

Prog

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

Crossrefs

Cf. A046801, A246600, A359080, A359081, A359083.

Sequence in context: A218190 A216757 A218366 * A359083 A218236 A218282

Adjacent sequences: A359079 A359080 A359081 * A359083 A359084 A359085

Keyword

nonn,base

Author

Amiram Eldar, Dec 15 2022

Extensions

a(28)-a(29) from Martin Ehrenstein, Dec 19 2022

Status

approved