A350631 - OEIS

%I #18 Jan 24 2022 16:04:51

%S 2,6,6,12,10,24,14,24,18,30,22,60,26,42,30,48,34,72,38,60,42,66,46,

%T 120,50,78,54,84,58,120,62,96,66,102,70,180,74,114,78,120,82,168,86,

%U 132,90,138,94,240,98,150,102,156,106,216,110,168,114,174,118,360,122,186,126

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

%C a(n) = min(A129902(n), A195199(n)).

%C Mostly agrees with A129902, but occasionally with A195199.

%C 698377680 is a value of n where a(n) is equal to A195199(n).

%C a(n) <= A053669(n)*n. - _David A. Corneth_, Jan 08 2022

%H Robert Israel, <a href="/A350631/b350631.txt">Table of n, a(n) for n = 1..10000</a>

%p f:= proc(n) local t,k;

%p     t:= 2*numtheory:-tau(n);

%p     for k from 2*n by n do

%p       if numtheory:-tau(k) >= t then return k fi

%p     od

%p end proc:

%p map(f, [$1..100]); # _Robert Israel_, Jan 20 2022

%t 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 *)

%o (PARI) a(n) = my(m=n, d=numdiv(n)); while(numdiv(m)<2*d, m+=n); m; \\ _Michel Marcus_, Jan 08 2022

%Y Cf. A000005, A129902, A195199.

%K nonn

%O 1,1

%A _J. Lowell_, Jan 08 2022