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
David A. Corneth, Table of n, a(n) for n = 1..53 (terms <= 10^30).
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
Bernard Schott, Jan 11 2021
EXTENSIONS
a(16)-a(20) from Michel Marcus, Jan 11 2021
a(21)-a(26) from Amiram Eldar, Jan 12 2021
a(27) from Chai Wah Wu, Jan 14 2021
More terms from David A. Corneth, Jan 15 2021
STATUS
approved