A211781 - OEIS

%I #17 Jan 10 2025 02:02:08

%S 2,3,4,5,7,11,13,17,19,23,27,29,31,37,41,43,47,53,59,61,67,71,73,79,

%T 83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,

%U 179,181,191,193,197,199,211,223,225,227,229,233,239,241,251,252

%N Numbers n such that Sum_(d_<n | n) tau(d_<n) / (d_<n) is an integer, where d_<n = divisors of n that are less than n, tau(x) = A000005(x).

%C Union primes (A000040) and sequence of composite numbers: 4, 27, 225, 252, 672, 1200, ...

%e Number 225 is in sequence because 1/1 + 2/3 + 2/5 + 3/9 + 4/15 + 3/25 + 6/45 + 6/75 = 3 (integer).

%t t = {}; Do[d2 = Sum[DivisorSigma[0,d]/d, {d, Most[Divisors[n]]}]; If[IntegerQ[d2], AppendTo[t, n]], {n, 2, 252}]; t (* _T. D. Noe_, Apr 26 2012 *)

%K nonn

%O 1,1

%A _Jaroslav Krizek_, Apr 20 2012