A355771 a(n) is the smallest integer that has exactly n divisors from A333369.

1, 3, 9, 15, 45, 105, 195, 315, 945, 900, 1575, 2100, 3900, 6825, 11655, 10500, 6300, 18900, 25200, 35100, 27300, 31500, 44100, 94500, 157500, 107100, 81900, 233100, 220500, 598500, 245700, 333900, 409500, 491400, 900900, 573300, 600600, 1228500, 1669500, 1965600

Offset

1,2

Links

Michael S. Branicky, Table of n, a(n) for n = 1..87

Example

15 has 4 divisors: {1, 3, 5, 15} all of which are in A333369 integers, and no smaller number has this property, hence a(4) = 15.

Mathematica

q[n_] := AllTrue[Tally @ IntegerDigits[n], EvenQ[Plus @@ #] &]; f[n_] := DivisorSum[n, 1 &, q[#] &]; 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[40, 10^7] (* Amiram Eldar, Jul 17 2022 *)

Prog

(PARI) issimber(m) = my(d=digits(m), s=Set(d)); for (i=1, #s, if (#select(x->(x==s[i]), d) % 2 != (s[i] % 2), return (0))); return (1); \\ A333369
a(n) = my(k=1); while (sumdiv(k, d, issimber(d)) != n, k++); k; \\ Michel Marcus, Jul 18 2022
(Python)
from sympy import divisors
from itertools import count, islice
def c(n): s = str(n); return all(s.count(d)%2 == int(d)%2 for d in set(s))
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(), 29))) # Michael S. Branicky, Jul 23 2022

Crossrefs

Cf. A333369, A353735, A355770, A355772, A355773.

Cf. A005231, A053624.

Similar sequences: A087997, A333456, A355303, A355699.

Sequence in context: A214771 A065917 A355772 * A053624 A348198 A119239

Adjacent sequences: A355768 A355769 A355770 * A355772 A355773 A355774

Keyword

nonn,base

Author

Bernard Schott, Jul 17 2022

Extensions

More terms from Amiram Eldar, Jul 17 2022

Status

approved