A195199 -id:A195199 - cp's OEIS frontend

A351126 a(n) = A195199(n) / n.

4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 10, 4, 6, 4, 6, 4, 8, 4, 6, 4, 6, 4, 10, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 10, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 10, 4, 6, 4, 6, 4, 8, 4, 6, 4, 6, 4, 12, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 10, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 10, 4

Offset: 1

J. Lowell, Feb 03 2022

nonn

a(n) = 4 for all odd n. For all even n, a(n) >= 6.

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Cf. A000005, A195199, A337686.

a[n_] := Module[{d = DivisorSigma[0, n], k = 1}, While[DivisorSigma[0, k*n] <= 2*d, k++]; k]; Array[a, 100] (* Amiram Eldar, Feb 03 2022 *)

a(n) = my(m=n, d=numdiv(n)); while(numdiv(m)<=2*d, m+=n); m/n; \\ Michel Marcus, Feb 27 2022

from math import prod
from collections import Counter
from itertools import count
from sympy import factorint
def A351126(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 # Chai Wah Wu, Feb 28 2022

A198186 Locations of records in A195199.

Original entry on oeis.org

1, 2, 4, 6, 8, 10, 12, 18, 24, 36, 48, 60, 84, 96, 108, 120, 156, 168, 180, 228, 240, 300, 360, 480, 600, 660, 720, 900, 960, 1080, 1320, 1380, 1440, 1620, 1800, 1920, 2160, 2400, 2520, 3360, 3840, 3960, 4320, 4680, 4800, 4860, 5040, 7560, 10080, 12600, 15120, 17640, 20160

Offset: 1

J. Lowell, Oct 21 2011

nonn

			20 does not qualify because A195199(18) = 144 and A195199(20) is only 120

Cf. A195199

A350631 a(n) is the smallest multiple of n that has at least twice as many divisors as n.

Original entry on oeis.org

2, 6, 6, 12, 10, 24, 14, 24, 18, 30, 22, 60, 26, 42, 30, 48, 34, 72, 38, 60, 42, 66, 46, 120, 50, 78, 54, 84, 58, 120, 62, 96, 66, 102, 70, 180, 74, 114, 78, 120, 82, 168, 86, 132, 90, 138, 94, 240, 98, 150, 102, 156, 106, 216, 110, 168, 114, 174, 118, 360, 122, 186, 126

Offset: 1

J. Lowell, Jan 08 2022

nonn

a(n) = min(A129902(n), A195199(n)).
Mostly agrees with A129902, but occasionally with A195199.
698377680 is a value of n where a(n) is equal to A195199(n).
a(n) <= A053669(n)*n. - David A. Corneth, Jan 08 2022

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000005, A129902, A195199.

f:= proc(n) local t,k;
    t:= 2*numtheory:-tau(n);
    for k from 2*n by n do
      if numtheory:-tau(k) >= t then return k fi
    od
end proc:
map(f, [$1..100]); # Robert Israel, Jan 20 2022

a[n_] := Module[{d = 2 * DivisorSigma[0, n], k = 2*n}, While[DivisorSigma[0, k] < d, k += n]; k]; Array[a, 100] (* Amiram Eldar, Jan 08 2022 *)

a(n) = my(m=n, d=numdiv(n)); while(numdiv(m)<2*d, m+=n); m; \\ Michel Marcus, Jan 08 2022

cp's OEIS Frontend

A351126 a(n) = A195199(n) / n.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Python

A198186 Locations of records in A195199.

Views

Author

Keywords

Examples

Crossrefs

A350631 a(n) is the smallest multiple of n that has at least twice as many divisors as n.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

PARI