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).
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
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
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Dec 15 2022
EXTENSIONS
a(28)-a(29) from Martin Ehrenstein, Dec 19 2022
STATUS
approved