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A359082
Indices of records in A246600.
8
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.
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