cp's OEIS Frontend

A355699 a(n) is the smallest number that has exactly n repdigit divisors.

%I A355699 #44 Aug 02 2024 12:04:09
%S A355699 1,2,4,6,12,24,72,66,666,132,1332,264,2664,792,13320,3960,14652,26664,
%T A355699 48840,29304,79992,341880,146520,399960,1333332,1025640,2799720,
%U A355699 8879112,2666664,18666648,7999992,44395560,13333320,93333240,39999960,279999720,269333064
%N A355699 a(n) is the smallest number that has exactly n repdigit divisors.
%H A355699 David A. Corneth, <a href="/A355699/b355699.txt">Table of n, a(n) for n = 1..135</a>
%H A355699 David A. Corneth, <a href="/A355699/a355699.gp.txt">PARI program</a>
%e A355699 72 has 12 divisors: {1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72}, only {1, 2, 3, 4, 6, 8, 9} are repdigits; no positive integer smaller than 72 has seven repdigit divisors, hence a(7) = 72.
%t A355699 f[n_] := DivisorSum[n, 1 &, Length[Union[IntegerDigits[#]]] == 1 &]; seq[len_, nmax_] := Module[{s = Table[0, {len}], c = 0, n = 1, i}, While[c < len && n < nmax, i = f[n]; If[i <= len && s[[i]] == 0, c++; s[[i]] = n]; n++]; s]; seq[24, 10^6] (* _Amiram Eldar_, Jul 15 2022 *)
%o A355699 (PARI) isrep(n) = 1==#Set(digits(n)); \\ A010785
%o A355699 a(n) = my(k=1); while (sumdiv(k, d, isrep(d)) != n, k++); k; \\ _Michel Marcus_, Jul 15 2022
%o A355699 (PARI) \\ See PARI link. - _David A. Corneth_, Jul 26 2022
%o A355699 (Python)
%o A355699 from sympy import divisors
%o A355699 from itertools import count, islice
%o A355699 def c(n): return len(set(str(n))) == 1
%o A355699 def f(n): return sum(1 for d in divisors(n, generator=True) if c(d))
%o A355699 def agen():
%o A355699     n, adict = 1, dict()
%o A355699     for k in count(1):
%o A355699         fk = f(k)
%o A355699         if fk not in adict: adict[fk] = k
%o A355699         while n in adict: yield adict[n]; n += 1
%o A355699 print(list(islice(agen(), 21))) # _Michael S. Branicky_, Jul 26 2022
%Y A355699 Cf. A010785, A087990, A190217, A340548, A355698.
%Y A355699 Similar sequences: A087997, A333456, A355303, A355695.
%K A355699 nonn,base,look
%O A355699 1,2
%A A355699 _Bernard Schott_, Jul 14 2022
%E A355699 a(9)-a(35) from _Michael S. Branicky_, Jul 14 2022
%E A355699 a(36)-a(37) from _Michael S. Branicky_, Jul 15 2022