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Non-prime-powers such that the number of composite divisors is a multiple of the number of prime divisors.
3

%I #11 Aug 31 2019 06:28:56

%S 36,100,120,144,168,196,225,264,270,280,312,324,378,400,408,440,441,

%T 456,484,520,552,576,594,616,676,680,696,702,728,744,750,760,784,888,

%U 918,920,945,952,960,984,1026,1032,1064,1089,1128,1144,1156,1160,1225,1240

%N Non-prime-powers such that the number of composite divisors is a multiple of the number of prime divisors.

%H Amiram Eldar, <a href="/A137945/b137945.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Reinhard Zumkeller)

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DivisorFunction.html">Divisor Function</a>

%F A055212(a(n)) mod A001221(a(n)) = 0.

%e A055212(120) = #{4,6,8,10,12,15,20,24,30,40,60,120} = 12 = 4*A001221(120) = 4*#{2,3,5} = 12, therefore 120 is a term.

%t aQ[n_] := (omega = PrimeNu[n]) > 1 && Divisible[DivisorSigma[0, n] - 1, omega]; Select[Range[2, 1240], aQ] (* _Amiram Eldar_, Aug 31 2019 *)

%Y Cf. A001221, A055212.

%Y Intersection of A024619 and A137944.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Feb 24 2008