A195199 Smallest multiple of n with more than twice as many divisors as n.

4, 12, 12, 24, 20, 36, 28, 48, 36, 60, 44, 120, 52, 84, 60, 96, 68, 144, 76, 120, 84, 132, 92, 240, 100, 156, 108, 168, 116, 180, 124, 192, 132, 204, 140, 360, 148, 228, 156, 240, 164, 252, 172, 264, 180, 276, 188, 480, 196, 300, 204, 312, 212, 432, 220, 336

Offset

1,1

Links

Table of n, a(n) for n=1..56.

Formula

a(n) = Min_{A000005(k*n) > 2*A000005(n)} k*n.

Example

a(4) must have more than 6 divisors because 4 has 3 divisors and 3*2=6. Therefore, it cannot be 16 because 16 has only 5 divisors.

Maple

A195199 := proc(n)
        for k from 2 do
                if numtheory[tau](k*n) > 2*numtheory[tau](n) then
                        return k*n ;
                end if;
        end do:
end proc: # R. J. Mathar, Oct 21 2011

Mathematica

Table[d = DivisorSigma[0, n]; m = 1; While[DivisorSigma[0, m*n] <= 2*d, m++]; m*n, {n, 100}] (* T. D. Noe, Oct 21 2011 *)

Prog

(PARI) a(n) = my(m=n, d=numdiv(n)); while(numdiv(m)<=2*d, m+=n); m; \\ Michel Marcus, Jan 08 2022
(Python)
from sympy import divisor_count
def a(n):
    dtarget, m = 2*divisor_count(n), 2*n
    while divisor_count(m) <= dtarget: m += n
    return m
print([a(n) for n in range(1, 57)]) # Michael S. Branicky, Jan 08 2022
(Python)
from math import prod
from itertools import count
from collections import Counter
from sympy import factorint
def A195199(n):
    f = Counter(factorint(n))
    d = prod(e+1 for e in f.values())
    for m in count(2):
        if prod(e+1 for e in (f+Counter(factorint(m))).values()) > 2*d:
            return m*n # Chai Wah Wu, Feb 28 2022

Crossrefs

Cf. A000005.

Sequence in context: A005886 A096442 A211437 * A294628 A323188 A284126

Adjacent sequences: A195196 A195197 A195198 * A195200 A195201 A195202

Keyword

nonn

Author

J. Lowell, Oct 12 2011

Status

approved