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A355716
a(n) is the smallest number that has exactly n binary palindrome divisors (A006995).
1
1, 3, 9, 15, 99, 45, 135, 189, 315, 495, 945, 765, 2079, 6237, 3465, 5355, 4095, 8415, 31185, 20475, 25245, 12285, 85995, 58905, 61425, 45045, 69615, 176715, 446985, 225225, 328185, 208845, 135135, 405405, 528255, 1396395, 675675, 2027025, 765765, 5360355, 2993445, 3968055, 3828825
OFFSET
1,2
LINKS
Michael S. Branicky, Table of n, a(n) for n = 1..67
EXAMPLE
a(4) = 15 since 15 has 4 divisors {1, 3, 5, 15} that are all palindromes when written in binary: 1, 11, 101 and 1111; no positive integer smaller than 15 has four divisors that are binary palindromes, hence a(4) = 15.
a(5) = 99 since 99 has 6 divisors {1, 3, 9, 11, 33, 99} of which only 11 is not a palindrome when written in binary: 11_10 = 1011_2; no positive integer smaller than 99 has five divisors that are binary palindromes, hence a(5) = 99.
MATHEMATICA
f[n_] := DivisorSum[n, 1 &, PalindromeQ[IntegerDigits[#, 2]] &]; 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[25, 10^5] (* Amiram Eldar, Jul 15 2022 *)
PROG
(PARI) is(n) = my(d=binary(n)); d==Vecrev(d); \\ A006995
a(n) = my(k=1); while (sumdiv(k, d, is(d)) != n, k++); k; \\ Michel Marcus, Jul 15 2022
(Python)
from sympy import divisors
from itertools import count, islice
def c(n): b = bin(n)[2:]; return b == b[::-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(), 20))) # Michael S. Branicky, Jul 23 2022
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Bernard Schott, Jul 15 2022
EXTENSIONS
More terms from Michael S. Branicky, Jul 15 2022
STATUS
approved