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

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

1,1

Comments

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

Links

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

Maple

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

Mathematica

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 *)

Prog

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

Crossrefs

Cf. A000005, A129902, A195199.

Sequence in context: A208570 A106832 A129902 * A087560 A071892 A064797

Adjacent sequences: A350628 A350629 A350630 * A350632 A350633 A350634

Keyword

nonn

Author

J. Lowell, Jan 08 2022

Status

approved