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A355695
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a(n) is the smallest number that has exactly n nonpalindromic divisors (A029742).
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3
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1, 10, 20, 30, 48, 72, 60, 140, 144, 120, 210, 180, 300, 240, 560, 504, 360, 420, 780, 1764, 900, 960, 720, 1200, 840, 1560, 2640, 1260, 1440, 2400, 3900, 3024, 1680, 3120, 2880, 4800, 7056, 3600, 2520, 3780, 3360, 5460, 6480, 16848, 6300, 8820, 7200, 9240, 6720, 12480, 5040
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OFFSET
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0,2
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LINKS
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EXAMPLE
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48 has 10 divisors: {1, 2, 3, 4, 6, 8, 12, 16, 24, 48}, only 12, 16, 24 and 48 are nonpalindromic; no positive integer smaller than 48 has four nonpalindromic divisors, hence a(4) = 48.
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MATHEMATICA
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f[n_] := DivisorSum[n, 1 &, ! PalindromeQ[#] &]; seq[len_, nmax_] := Module[{s = Table[0, {len}], c = 0, n = 1, i}, While[c < len && n < nmax, i = f[n] + 1; If[i <= len && s[[i]] == 0, c++; s[[i]] = n]; n++]; s]; seq[50, 10^5] (* Amiram Eldar, Jul 14 2022 *)
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PROG
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(PARI) isnp(n) = my(d=digits(n)); d!=Vecrev(d); \\ A029742
a(n) = my(k=1); while (sumdiv(k, d, isnp(d)) != n, k++); k; \\ Michel Marcus, Jul 14 2022
(Python)
from sympy import divisors
from itertools import count, islice
def c(n): s = str(n); return s != s[::-1]
def f(n): return sum(1 for d in divisors(n, generator=True) if c(d))
def agen():
n, adict = 0, 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
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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