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

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

Offset: 0

Author

Bernard Schott, Jul 14 2022

Keywords

• nonn
• base

Examples

			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.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 0..710

Crossrefs

Cf. A029742, A087991, A093037, A334391.

Similar sequences: A087997, A333456, A355303, A355594.

Programs

Mathematica

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 *)

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
print(list(islice(agen(), 51))) # Michael S. Branicky, Jul 27 2022

Extensions

More terms from Michel Marcus, Jul 14 2022