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A355695 a(n) is the smallest number that has exactly n nonpalindromic divisors (A029742).

%I A355695 #16 Jul 27 2022 13:33:00
%S A355695 1,10,20,30,48,72,60,140,144,120,210,180,300,240,560,504,360,420,780,
%T A355695 1764,900,960,720,1200,840,1560,2640,1260,1440,2400,3900,3024,1680,
%U A355695 3120,2880,4800,7056,3600,2520,3780,3360,5460,6480,16848,6300,8820,7200,9240,6720,12480,5040
%N A355695 a(n) is the smallest number that has exactly n nonpalindromic divisors (A029742).
%H A355695 Michael S. Branicky, <a href="/A355695/b355695.txt">Table of n, a(n) for n = 0..710</a>
%e A355695 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.
%t A355695 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 *)
%o A355695 (PARI) isnp(n) = my(d=digits(n)); d!=Vecrev(d); \\ A029742
%o A355695 a(n) = my(k=1); while (sumdiv(k, d, isnp(d)) != n, k++); k; \\ _Michel Marcus_, Jul 14 2022
%o A355695 (Python)
%o A355695 from sympy import divisors
%o A355695 from itertools import count, islice
%o A355695 def c(n): s = str(n); return s != s[::-1]
%o A355695 def f(n): return sum(1 for d in divisors(n, generator=True) if c(d))
%o A355695 def agen():
%o A355695     n, adict = 0, dict()
%o A355695     for k in count(1):
%o A355695         fk = f(k)
%o A355695         if fk not in adict: adict[fk] = k
%o A355695         while n in adict: yield adict[n]; n += 1
%o A355695 print(list(islice(agen(), 51))) # _Michael S. Branicky_, Jul 27 2022
%Y A355695 Cf. A029742, A087991, A093037, A334391.
%Y A355695 Similar sequences: A087997, A333456, A355303, A355594.
%K A355695 nonn,base
%O A355695 0,2
%A A355695 _Bernard Schott_, Jul 14 2022
%E A355695 More terms from _Michel Marcus_, Jul 14 2022