The On-Line Encyclopedia of Integer Sequences (OEIS)

A355771 revision #30

A355771

a(n) is the smallest integer that has exactly n simbers divisors.

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

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OFFSET

1,2

COMMENTS

The word simber (A333369) comes from Project Euler in link.

The six first terms are also the six first highly composite odd numbers (A053624).

LINKS

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

Project Euler, Problem 520: Simbers.

EXAMPLE

15 has 4 divisors: {1, 3, 5, 15} all of which are simbers integers; no positive integer smaller than 15 has four simber divisors, 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)