%I #8 Aug 07 2017 23:15:23

%S 1,2,9,10,26,34,46,76,121,128,136,140,174,194,226,230,232,240,268,278,

%T 296,325,362,370,432,434,438,575,598,610,620,637,694,708,718,734,735,

%U 756,796,808,842,854,860,866,898,922,925,986,1048,1050,1072,1168,1196,1228

%N Numbers x such that x = Sum_{j=1..k} d(j*x), for some k, where d(x) is the number of divisors of x.

%C Values of k for the listed items are 1, 1, 2, 2, 4, 5, 6, 7, 14, 9, 9, 7, 11, 19, 21, 13, 14, 8, 19, 25, 17, 18, 31, 19, 13, 21, 23, 29, 27, 28, 22, 31, 53, 26, 54, 55, 23, 17, 45, 38, 62, 36, 29, 63, 65, 66, 42, 40, 47, 21, 41, 44, 36, 65.

%C All squarefree terms > 1 are even. - _Robert Israel_, Aug 07 2017

%H Robert Israel, <a href="/A290592/b290592.txt">Table of n, a(n) for n = 1..1000</a>

%e For 34 we have that d(34) + d(2*34) + d(3*34) + d(4*34) + d(5*34) = 4 + 6 + 8 + 8 + 8 = 34.

%p with(numtheory): P:=proc(n) local a,k; a:=0; k:=0; while a<n do k:=k+1;

%p a:=a+tau(k*n); od; if a=n then n; fi; end: seq(P(i),i=1..2000);

%Y Cf. A000005, A270713, A270389.

%K nonn,easy

%O 1,2

%A _Paolo P. Lava_, Aug 07 2017