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A195199 Smallest multiple of n with more than twice as many divisors as n. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 15 02:47 EDT 2022. Contains 356122 sequences. (Running on oeis4.)