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A357035
a(n) is the smallest number that has exactly n divisors that are digitally balanced numbers (A031443).
2
1, 2, 10, 36, 150, 180, 420, 840, 900, 3420, 2520, 5040, 6300, 7560, 12600, 15120, 18900, 42840, 32760, 37800, 95760, 105840, 69300, 124740, 163800, 138600, 166320, 327600, 249480, 207900, 491400, 622440, 498960, 706860, 415800, 963900, 1496880, 1164240, 1081080
OFFSET
0,2
LINKS
EXAMPLE
1 has no divisors in A031443, so a(0) = 1;
2 has divisors 1 = 1_2, 2 = 10_2 and 2 = A031443(1), so a(1) = 2.
10 has divisors 2 = 10_2 and 10 = 1010_2 in A031443, so a(2) = 10.
MAPLE
N:= 20: # for terms before the first term >= 2^(N+1)
W:= Vector(2^(N+1), datatype=integer[4]):
for d from 2 to N by 2 do
for t from 2^(d-1) to 2^d-1 do
if convert(convert(t, base, 2), `+`) = d/2 then
J:= [seq(i, i=t..2^(N+1), t)];
W[J]:= W[J] +~ 1;
fi od od:
M:= max(W);
V:= Array(0..M); count:= 0:
for i from 1 to 2^(N+1) do
if V[W[i]] = 0 then V[W[i]]:= i; count:= count+1 fi
od:
L:= convert(V, list):
if not member(0, L, 'm') then m:= M+2 fi:
L[1..m-1]; # Robert Israel, Sep 27 2023
MATHEMATICA
digBalQ[n_] := Module[{d = IntegerDigits[n, 2], m}, EvenQ @ (m = Length[d]) && Count[d, 1] == m/2]; f[n_] := DivisorSum[n, 1 &, digBalQ[#] &]; seq[len_, nmax_] := Module[{s = Table[0, {len}], c = 0, n = 1, i}, While[c < len && n < nmax, i = f[n] + 1; If[i <= len && s[[i]] == 0, c++; s[[i]] = n]; n++]; s]; seq[40, 10^7] (* Amiram Eldar, Sep 26 2022 *)
PROG
(Magma) bal:=func<n|Multiplicity(Intseq(n, 2), 1) eq Multiplicity(Intseq(n, 2), 0)>; a:=[]; for n in [0..38] do k:=1; while #[d:d in Divisors(k)|bal(d)] ne n do k:=k+1; end while; Append(~a, k); end for; a;
CROSSREFS
Cf. A031443.
Sequence in context: A202796 A335559 A001582 * A370713 A026546 A256105
KEYWORD
nonn,base
AUTHOR
Marius A. Burtea, Sep 20 2022
EXTENSIONS
Corrected by Robert Israel, Sep 27 2023
STATUS
approved