|
| |
|
|
A340548
|
|
Integers whose number of repdigit divisors sets a new record.
|
|
10
|
|
|
|
1, 2, 4, 6, 12, 24, 66, 132, 264, 792, 3960, 14652, 26664, 29304, 79992, 146520, 399960, 1025640, 2666664, 7999992, 13333320, 39999960, 269333064, 807999192, 1346665320, 4039995960, 28279971720, 7999999999992, 8080799919192, 13333333333320, 13467999865320, 39999999999960, 40403999595960
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
The first 10 terms are the same as A093036, then A093036(11) = 1848 while a(11) = 3960, because from a(1) to a(10), all palindromic divisors are also repdigits, and then 616 is a non-repdigit palindromic divisor of 1848.
Number of repdigit divisors: 1, 2, 3, 4, 5, 6, 8, 10, 12, 14, 16, 17, 18, ...
Indices of repdigits: 1, 2, 3, 4, 7, ...
|
|
|
LINKS
|
|
|
|
EXAMPLE
|
132 has 12 divisors: {1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132} of which 10 are repdigits: {1, 2, 3, 4, 6, 11, 22, 33, 44, 66}. No positive integer smaller than 132 has as many as ten repdigit divisors; hence 132 is a term.
|
|
|
MATHEMATICA
|
repQ[n_] := Length @ Union @ IntegerDigits[n] == 1; s[n_] := DivisorSum[n, 1 &, repQ[#] &]; smax = 0; seq = {}; Do[s1 = s[n]; If[s1 > smax, smax = s1; AppendTo[seq, n]], {n, 1, 10^5}]; seq (* Amiram Eldar, Jan 11 2021 *)
|
|
|
PROG
|
(PARI) isrd(n) = {1 == #Set(digits(n))}; \\ A010785
f(n) = sumdiv(n, d, isrd(d));
lista(nn) = {my(m = 0); for (n=1, nn, my(x = f(n)); if (x > m, print1(n, ", "); m = x); ); } \\ Michel Marcus, Jan 11 2021
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,base
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
