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A340548 Integers whose number of repdigit divisors sets a new record.

%I A340548 #58 Jan 15 2021 17:55:37
%S A340548 1,2,4,6,12,24,66,132,264,792,3960,14652,26664,29304,79992,146520,
%T A340548 399960,1025640,2666664,7999992,13333320,39999960,269333064,807999192,
%U A340548 1346665320,4039995960,28279971720,7999999999992,8080799919192,13333333333320,13467999865320,39999999999960,40403999595960
%N A340548 Integers whose number of repdigit divisors sets a new record.
%C A340548 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.
%C A340548 Number of repdigit divisors: 1, 2, 3, 4, 5, 6, 8, 10, 12, 14, 16, 17, 18, ...
%C A340548 Indices of repdigits: 1, 2, 3, 4, 7, ...
%H A340548 David A. Corneth, <a href="/A340548/b340548.txt">Table of n, a(n) for n = 1..53</a> (terms <= 10^30).
%e A340548 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.
%t A340548 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 *)
%o A340548 (PARI) isrd(n) = {1 == #Set(digits(n))}; \\ A010785
%o A340548 f(n) = sumdiv(n, d, isrd(d));
%o A340548 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
%Y A340548 Cf. A010785, A190217.
%Y A340548 Similar for: A053624 (odd), A181808 (even), A093036 (palindromes), A340549 (repunits).
%K A340548 nonn,base
%O A340548 1,2
%A A340548 _Bernard Schott_, Jan 11 2021
%E A340548 a(16)-a(20) from _Michel Marcus_, Jan 11 2021
%E A340548 a(21)-a(26) from _Amiram Eldar_, Jan 12 2021
%E A340548 a(27) from _Chai Wah Wu_, Jan 14 2021
%E A340548 More terms from _David A. Corneth_, Jan 15 2021