A355699 a(n) is the smallest number that has exactly n repdigit divisors.
1, 2, 4, 6, 12, 24, 72, 66, 666, 132, 1332, 264, 2664, 792, 13320, 3960, 14652, 26664, 48840, 29304, 79992, 341880, 146520, 399960, 1333332, 1025640, 2799720, 8879112, 2666664, 18666648, 7999992, 44395560, 13333320, 93333240, 39999960, 279999720, 269333064
Offset: 1
Examples
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.
Links
- David A. Corneth, Table of n, a(n) for n = 1..135
- David A. Corneth, PARI program
Crossrefs
Programs
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Mathematica
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 *) -
PARI
isrep(n) = 1==#Set(digits(n)); \\ A010785 a(n) = my(k=1); while (sumdiv(k, d, isrep(d)) != n, k++); k; \\ Michel Marcus, Jul 15 2022
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PARI
\\ See PARI link. - David A. Corneth, Jul 26 2022
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Python
from sympy import divisors from itertools import count, islice def c(n): return len(set(str(n))) == 1 def f(n): return sum(1 for d in divisors(n, generator=True) if c(d)) def agen(): n, adict = 1, dict() for k in count(1): fk = f(k) if fk not in adict: adict[fk] = k while n in adict: yield adict[n]; n += 1 print(list(islice(agen(), 21))) # Michael S. Branicky, Jul 26 2022
Extensions
a(9)-a(35) from Michael S. Branicky, Jul 14 2022
a(36)-a(37) from Michael S. Branicky, Jul 15 2022